Név: Ágoston István

MSc in mathematics: List of courses

(B) Basic courses (20 credits)

Subject	Hours	Credits	Coordinator
Analysis 4 (BSc)	4+2	4+2	János Kristóf
Basic algebra (reading course)	0+2	5	Péter Pál Pálfy
Basic geometry (reading course)	0+2	5	Gábor Moussong
Complex functions (BSc)	3+2	3+2	Gábor Halász
Differentialgeometry I. (BSc)	2+2	2+3	László Verhóczki
Geometry III. (BSc)	3+2	3+2	Balázs Csikós
Intorduction to topology (BSc)	2+0	2	András Szűcs
Probability and statistics	3+2	3+3	Tamás Móri
Reading course in analysis	0+2	5	Árpád Tóth
Set theory (BSc)	2+0	2	Péter Komjáth

(C) Core courses (at least 30 credits from at least 4 different subject groups)

Subject	Hours	Credits	Coordinator
Algebra and number theory
Groups and representations	2+2	2+3	Péter Pál Pálfy
Number theory II	2+0	2	András Sárközy
Rings and algebras	2+2	2+3	István Ágoston
Analysis
Function series	2+0	2	János Kristóf
Fourier-integral	2+1	2+1	Gábor Halász
Functional analysis II	1+2	1+2	Zoltán Sebestyén
Topics in analysis	2+1	2+2	Tamás Keleti
Geometry
Algebraic topology	2+0	2	András Szűcs
Combinatorial geometry	2+1	2+2	György Kiss
Differential geometry II.	2+0	2	László Verhóczki
Differential topology	2+0	2	András Szűcs
Topics in differential geometry	2+0	2	Balázs Csikós
Stochastics
Discrete parameter martingales	2+0	2	Tamás Móri
Markov chains in discrete and continuous time	2+0	2	Vilmos Prokaj
Multivariate statistical methods	4+0	4	György Michaletzky
Statistical computing 1	0+2	3	András Zempléni
Discrete mathematics
Algorithms I	2+2	2+3	Zoltán Király
Discrete mathematics	2+2	2+3	László Lovász
Mathematical logic	2+0	2	Péter Komjáth
Operations research
Continuous optimization	3+2	3+3	Tibor Illés
Discrete optimization	3+2	3+3	András Frank

(D) Differentiated courses (at least 44 credits from at least 3 different subject groups)

Subject	Hours	Credits	Coordinator
Algebra
Commutative algebra	2+2	3+3	József Pelikán
Current topics in algebra	2+0	3	Emil Kiss
Topics in group theory	2+2	3+3	Péter Pál Pálfy
Topics in ring theory	2+2	3+3	István Ágoston
Universal algebra and lattice theory	2+2	3+3	Emil Kiss
Number theory
Combinatorial number theory	2+0	3	András Sárközy
Exponential sums in number theory	2+0	3	András Sárközy
Multiplicative number theory	2+0	3	Mihály Szalay
Analysis
Chapters of complex function theory	4+0	6	Gábor Halász
Complex manifolds	3+2	4+3	Róbert Szőke
Descriptive set theory	3+2	4+3	Miklós Laczkovich
Discrete dinamcal systems	2+0	3	Zoltán Buczolich
Dynamical systems	2+0	3	Zoltán Buczolich
Dynamical systems and differential equations	4+2	6+3	Péter Simon
Dynamics in one complex variable	2+0	3	István Sigray
Ergodic theory	2+0	3	Zoltán Buczolich
Geometric measure theory	3+2	4+3	Tamás Keleti
Nonlinear functional analysis and its applications	3+2	4+3	János Karátson
Operator semigroups	2+2	3+3	András Bátkai
Partial differential equations	4+2	6+3	László Simon
Representations of Banach*-algebras and abstract harmonic analysis	2+1	2+2	János Kristóf
Riemann manifolds	2+0	3	Róbert Szőke
Seminar in complex analysis	0+2	2	Róbert Szőke
Special functions	2+0	3	Gábor Halász
Topological vector spaces and Banach algebras	2+2	3+3	János Kristóf
Unbounded operators of Hilbert spaces	2+0	3	Zoltán Sebestyén
Geometry
Algebraic and differential topology	4+2	6+3	András Szűcs
Convex geometry	4+2	6+3	Károly Böröczky Jr.
Differential toplogy problem solving	0+2	3	András Szűcs
Discrete geometry	3+2	4+3	Károly Bezdek
Finite geometries	2+0	3	György Kiss
Geometric foundations of 3D graphics	2+2	3+3	György Kiss
Geometric modelling	2+0	3	László Verhóczki
Lie groups and symmetric spaces	4+2	6+3	László Verhóczki
Riemannian geometry	4+2	6+3	Balázs Csikós
Supplementay chapters of topology I – toplogy of singularities	2+0	3	András Némethi
Supplementay chapters of topology II – low dimensional topology	2+0	3	András Stipsicz
Stochastics
Analysis of time series	2+2	3+3	László Márkus
Cryptography	2+0	3	István Szabó
Introduction to information theory	2+0	3	István Szabó
Statistical computing 2	0+2	3	András Zempléni
Statistical hypothesis testing	2+0	3	Villő Ciszár
Stochastic processes with independent increment, limit theorems	2+0	3	Vilmos Prokaj
Discrete mathematics
Applied discrete mathematics seminar	0+2	2	Zoltán Király
Codes and symmetric structures	2+0	3	Tamás Szőnyi
Complexity theory	2+2	3+3	Vince Grolmusz
Complexity theory seminar	0+2	2	Vince Grolmusz
Data mining	2+2	3+3	András Lukács
Design, analysis and implementation of algorithms and data structures I	2+2	3+3	Zoltán Király
Design, analysis and implementation of algorithms and data structures II	2+0	3	Zoltán Király
Discrete mathematics II	4+0	6	Tamás Szőnyi
Geometric algorithms	2+0	3	Katalin Vesztergombi
Graph theory seminar	0+2	2	László Lovász
Mathematics of networks and the WWW	2+0	3	András Benczúr
Selected topics in graph theory	2+0	3	László Lovász
Set theory I	4+0	6	Péter Komjáth
Set theory II	4+0	6	Péter Komjáth
Operations research
Applications of operation research	2+0	3	Gergely Mádi-Nagy
Approximation algorithms	2+0	3	Tibor Jordán
Business Economics	2+0	3	Róbert Fullér
Combinatorial algorithms I.	2+2	3+3	Tibor Jordán
Combinatorial algorithms II.	2+0	3	Tibor Jordán
Combinatorial structures and algorithms	0+2	3	Tibor Jordán
Computational methods in operation reserach	0+2	3	Gergely Mádi-Nagy
Game theory	2+0	3	Tibor Illés
Graph theory	2+0	3	András Frank, Zoltán Király
Graph theory tutorial	0+2	3	András Frank, Zoltán Király
Integer programming I.	2+0	3	Tamás Király
Integer programming II.	2+0	3	Tamás Király
Inventory management	2+0	3	Gergely Mádi-Nagy
Investments analysis	0+2	3	Róbert Fullér
LEMON library: Solving optimization problems in C++	0+2	3	Alpár Jüttner
Linear optimization	2+0	3	Tibor Illés
Macroeconomics and the theory of economic equilibrium	2+0	3	Gergely Mádi-Nagy
Manufacturing process management	2+0	3	Tamás Király
Market analysis	2+0	3	Róbert Fullér
Matroid theory	2+0	3	András Frank
Microeconomy	2+0	3	Gergely Mádi-Nagy
Multiple objective optimization	0+2	3	Róbert Fullér
Nonliear optimization	3+0	4	Tibor Illés
Operations research project	0+2	3	Róbert Fullér
Polyhedral combinatorics	2+0	3	Tamás Király
Scheduling theory	2+0	3	Tibor Jordán
Stochastic optimization	2+0	3	Csaba Fábián
Stochastic optimization practice	0+2	3	Csaba Fábián
Structures in combinatorial optimization	2+0	3	Tibor Jordán

MSc in matematics: Examples

The following two sequences of courses illustrate how the credit requirements of the MSc program can be fulfilled.

Subject area	Subject	Level	Hours	Credits
1. term

Algebra	Groups and representations	C	2+2	5
Analysis	Functional analysis	C	1+2	4
Analysis	Topics in analysis	C	2+1	4
Analysis	Algebraic topology	C	2+0	2
Analysis	Differential topology	C	2+0	2
Analysis	Chapters of complex function theory	D	4+0	6
Analysis	Differential topology problem solving	D	0+2	3
	General subject	G	2+0	2

	Total:		22	28
	Number of exams: 7

Subject area	Subject	Level	Hours	Credits
2. term
Algebra.	Algebraic and differential topology	D	4+2	9
Stochastics.	Introduction to information theory	D	2+0	3
Analysis	Topological vector spaces and Banach algebras	D	2+2	6
Analysis.	Nonlinear functional analysis	D	3+2	7
	Special course	O	2+0	2
	General subject	G	2+0	2

	Total:		21	29
	Number of exams: 6

Subject area	Subject	Level	Hours	Credits
3. term
Operations research	Continuous optimization	C	3+2	7
Discrete mathematics	Discrete mathematics.	C	2+2	5
Geometry	Topics in differential geometry	C	2+0	2
Analysis	Riemann surfaces	D	2+0	3
Algebra	Topics in ring theory	D	2+0	3
Discrete mathematics	Set theory I.	D	4+0	6
	General subject	G	2+0	2

	Total:		21	28
	Number of exams: 7

Subject area	Subject	Level	Hours	Credits
4. term
Geometry	Geometric measure theory	D	3+2	7
Analysis.	Complex manifolds	D	3+2	7
Discrete mathematics	Set theory II.	D	4+0	6

	Total:		14	20
	Number of exams: 3

Subject area	Subject	Level	Hours	Credits
1. term
Analysis	Analysis 4.	B	4+2	6
Algebra	Basic algebra (reading course)	B	0+2	5
Geometry	Differential geometry I.	B	2+2	5
Stochastics	Probablity and statistics	B	3+2	6
	General subject	G	2+0	2

	Total:		19	24
	Number of exams: 5


Subject area	Subject	Level	Hours	Credits
2. term
Probablity theory	Multivariate statistical methods	C	4+0	5
Probablity theory	Statistical computing 1.	C	0+2	2
Geometry	Discrete geometry	D	3+2	7
Stochastics	Introduction to information theory	D	2+0	3
Analysis	Topological vector spaces and Banach algebras	D	2+2	6
	General subject	G	2+0	2

	Total:		19	25
	Number of exams: 5


Subject area	Subject	Level	Hours	Credits
3. term
Analysis	Functional analysis	C	1+2	4
Analysis	Topics in analysis	C	2+1	4
opkut.	Continuous optimization	C	3+2	6
Algebra	Groups and representations	C	2+2	5
számtud.	Discrete mathematics	C	2+2	5
Stochastics	Cryptography	D	2+0	3
	General subject	G	2+0	2

	Total:		23	29
	Number of exams: 7


Subject area	Subject	Level	Hours	Credits
4. term
Analysis	Nonlinear functional analysis	D	3+2	6
Algebra	Exponential sums in number theory	D	2+0	3
Geometry	Geometric measure theory	D	3+2	7
Analysis	Complex manifolds	D	3+2	7

	Total:		17	23
	Number of exams: 4

MSc in matematics: Personal conditions

Program coordinator, subprogram coordinators,coordinators of final exams

Name of coordinators and type of responsibility

( pc: program coordinator,

spc: subprgram coordinator with given subprogram,

fec: coordinator of final exam)

Degree/title

Position

Type of employment

Number of coordinated programs

Total credit value of BSc and MSc courses coordinated by the lecturer: in this program / in this institution / in Hungary

András Szűcs

acad.

full professor

16/22/22

Course list – coordinators, lecturers

*Course names* *(Basic and Core courses*)		Lecturers
*Course names* *(Basic and Core courses*)		Lecturers (For each subject block the first name stands for the coordinator’s name)	Degree / title		Position	Type of employment	Giving lectures Y/N	Giving tutorials Y/N	Total credit value of BSc and MSc courses coordinated by the lecturer: in this program / in this institution / in Hungary
MSc in mathematics
Basic courses	1. Analysis IV (BSc)	Kristóf János	CSc	assoc. prof.		FT	Y	Y	18/18/18
		Miklós Laczkovich	acad.	full prof.		FT	Y	N	7/22/22
		Zoltán Sebestyén	DSc	full prof.		FT	Y	Y	6/10/10
		János Karátson	PhD	assoc. prof.		FT	Y	Y	7/20/20
		Tamás Keleti	PhD	assoc. prof.		FT	Y	Y	7/16/16
		Péter Simon	PhD	assoc. prof.		FT	Y	Y	9/22/22
		András Bátkai	PhD	sen. asst. prof.		FT	N	Y	6/11/11
		László Fehér	PhD	sen. asst. prof.		FT	N	Y	–
		Árpád Tóth	PhD	sen. asst. prof.		FT	N	Y	5/5/5
		Eszter Sikolya	PhD	asst. prof.		FT	N	Y	–
		Ferenc Izsák	PhD	asst. prof.		FT	N	Y	–
		István Sigray	PhD	lecturer		FT	N	Y	3/3/3
	2. Complex functions(BSc)	Gábor Halász	acad.	full prof.		FT	Y	N	13/24/24
		Róbert Szőke	CSc	assoc. prof.		FT	Y	Y	13/20/20
		Árpád Tóth	PhD	sen. asst. prof.		FT	N	Y	5/5/5
		István Sigray	PhD	lecturer		FT	N	Y	3/3/3
	3. Introduction to topology (BSc)	András Szűcs	acad	full prof.		FT	Y	N	16/22/22
		Róbert Szőke	CSc	assoc. prof.		FT	Y	N	13/20/20
		László Fehér	PhD	sen. asst. prof.		FT	Y	N	–
		Árpád Tóth	PhD	sen. asst. prof.		FT	Y	N	5/5/5
	4. Reading course in analysis	Árpád Tóth	PhD	assoc. prof.		FT	Y	Y	5/5/5
	4. Reading course in analysis	László Fehér	PhD	sen. asst. prof.		FT	Y	Y	–
	5. Geometry III. (BSc)	Balázs Csikós	CSc	assoc. prof.		FT	Y	Y	9/25/25
		Gábor Moussong	PhD	sen. asst. prof.		FT	Y	Y	5/5/5
		Gyula Lakos	PhD	asst. prof.		FT	N	Y	–
	6. Differential geometry (BSc)	László Verhóczki	PhD	assoc. prof.		FT	Y	Y	12/24/24
		Balázs Csikós	CSc	assoc. prof.		FT	Y	Y	9/25/25
		Gábor Moussong	PhD	sen. asst. prof.		FT	Y	Y	5/5/5
	7. Set theory (intorductory) (BSc)	Péter Komjáth	DSc	full prof.		FT	Y	N	12/20/20
	8. Probability and statistics	Tamás Móri	CSc	assoc. prof.		FT	Y	Y	8/25/25
		György Michaletzky	DSc	full prof.		FT	Y	N	4/24/24
		András Zempléni	CSc	assoc. prof.		FT	Y	Y	6/24/24
		Miklós Arató	CSc	assoc. prof.		FT	Y	Y	0/26/26
	9. Basic algebra (reading course)	Péter Pál Pálfy	acad.	full prof.		O	Y	Y	11/22/22
		István Ágoston	CSc	assoc. prof.		FT	Y	Y	11/11/11
		Emil Kiss	DSc	full prof.		FT	Y	Y	9/23/23
		József Pelikán	dr. univ	sen. asst. prof.		FT	Y	Y
		Csaba Szabó	DSc	assoc. prof.		FT	Y	Y
	10. Basic geometry	Gábor Moussong	PhD	Sen. Asst. prof.		FT	Y	Y	5/5/5
		Károly Bezdek	DSc	full prof.		FT	Y	Y	7/12/12
		Károly Böröczky Jr.	DSc	assoc. prof.		O	Y	Y	11/11/11
		Balázs Csikós	CSc	assoc. prof.		FT	Y	Y	9/25/25
		Gábor Kertész	dr. univ	sen. asst. prof.		FT	Y	Y	–
		György Kiss	PhD	assoc. prof.		FT	Y	Y	13/18/18

*Course names* *(Basic and Core courses*)			Lecturers
*Course names* *(Basic and Core courses*)			Lecturers (For each subject block the first name stands for the coordinator’s name)	Degree / title	Position	Type of employment	Giving lectures Y/N	Giving tutorials Y/N	Total credit value of BSc and MSc courses coordinated by the lecturer: in this program / in this institution / in Hungary
MSc in mathematics
Core corses	1. Groups and representations	Péter Pál Pálfy		acad.	full prof.	O	Y	Y	11/22/22
		Piroska Csörgő		CSc	assoc. prof.	FT	N	Y	–
		Péter Hermann		CSc	assoc. prof.	FT	Y	Y	–
		József Pelikán		dr. univ.	sen. asst. prof.	FT	Y	Y	6/6/6
		Csaba Szabó		DSc	assoc. prof.	FT	Y	Y	–
	2. Rings and algebras	István Ágoston		CSc	assoc. prof.	FT	Y	Y	11/11/11
		Emil Kiss		DSc	full prof.	FT	Y	Y	9/23/23
		József Pelikán		dr. univ.	sen. asst. prof.	FT	Y	Y	6/6/6
	3. Number theory II (BSC)	András Sárközy		acad.	full prof.	FT	Y	Y	6/16/16
		Róbert Freud		CSc	assoc. prof.	FT	Y	Y	0/8/8
		Gyula Károlyi		CSc	assoc. prof.	FT	N	Y	0/4/4
		Katalin Pappné Kovács		CSc	assoc. prof.	FT	N	Y	–
		Mihály Szalay		CSc	assoc. prof.	FT	Y	Y	3/7/7
	4. Fourier integral	Gábor Halász		acad.	full prof.	FT	Y		13/24/24
		Róbert Szőke		CSc	assoc. prof.	FT	Y	Y	13/20/20
		István Sigray		PhD	lecturer	FT	Y		3/3/3
		Árpád Tóth		PhD	assoc. prof.	FT	Y		5/5/5
	5. Topics in analysis	Tamás Keleti		PhD	assoc. prof.	FT	Y		7/16/16
		Miklós Laczkovich		acad.	full prof.	FT	Y		7/22/22
		Zoltán Buczolich		CSc	assoc. prof.	FT	Y	Y	9/19/19
	6. Topics in differential geometry	Balázs Csikós		CSc	assoc. prof.	FT	Y		9/25/25
		Gyula Lakos		PhD	asst. prof.	FT	N		–
		Gábor Moussong		PhD	sen. asst. prof.	FT	Y		5/5/5
		László Verhóczki		PhD	assoc. prof.	FT	Y		12/24/24
	7. Differential Geometry II.	László Verhóczki		PhD	assoc. prof.	FT	Y		12/24/24
		Balázs Csikós		CSc	assoc. prof.	FT	Y		9/25/25
		Gyula Lakos		PhD	asst. prof.	FT	N		–
		Gábor Moussong		PhD	sen. asst. prof.	FT	Y		5/5/5
	8. Combinatorial geometry	György Kiss		PhD	assoc. prof.	FT	Y	Y	13/18/18
		Károly Böröczky Jr.		DSc	assoc. prof.	O	Y	Y	11/11/11
		Gábor Kertész		dr. univ	sen. asst. prof.	FT	Y	Y	–
	9. Algebraic topology	András Szűcs		acad.	full prof.	FT	Y		16/22/22
		Balázs Csikós		CSc	assoc. prof.	FT	Y		9/25/25
		László Fehér		PhD	sen. asst. prof.	FT	Y		–
		Gábor Moussong		PhD	sen. asst. prof.	FT	Y		5/5/5
		András Némethi		DSc	sci. advisor	O	Y		3/3/3
		András Stipsicz		DSc	sen. res. fellow	O	Y		3/3/3
		Róbert Szőke		CSc	assoc. prof.	FT	Y	Y	13/20/20
		Árpád Tóth		PhD	assoc. prof.	FT	Y		5/5/5
	10. Differential topology	András Szűcs		acad	full prof.	FT	Y		16/22/22
		Balázs Csikós		CSc	assoc. prof.	FT	Y		9/25/25
		László Fehér		PhD	sen. asst. prof.	FT	Y		–
		Gábor Moussong		PhD	sen. asst. prof.	FT	Y		5/5/5
		András Némethi		DSc	sci. advisor	O	Y		3/3/3
		András Stipsicz		DSc	tud. fmtárs	O	Y		3/3/3
		Árpád Tóth		PhD	assoc. prof.	FT	Y		5/5/5
	11. Mathematical logic	Péter Komjáth		DSc	full prof.	FT	Y	N	12/20/20
	12. Markov chains in discrete and continuous time	Vilmos Prokaj		PhD	assoc. prof.	FT	Y	N	5/23/23
		György Michaletzky		DSc	full prof.	FT	Y	N	4/24/24
		Villő Csiszár			asst. prof.	FT	Y	N	3/3/3
	13. Discrete parameter martingales	Tamás Móri		CSc	assoc. prof.	FT	Y	N	8/25/25
		Vilmos Prokaj		PhD	assoc. prof.	FT	Y	N	5/23/23
		György Michaletzky		DSc	full prof.	FT	Y	N	4/24/24
	14. Statistical computing 1.	András Zempléni		CSc	assoc. prof.	FT	N	Y	6/24/24
	14. Statistical computing 1.	Tamás Pröhle			asst. prof.	FT	N	Y	–
	15. Multivariate statistical methods	György Michaletzky		DSc	full prof.	FT	Y	N	4/24/24
		Miklós Arató		CSc	assoc. prof.	FT	Y	N	0/26/26
		Tamás Pröhle			asst. prof.	FT	Y	N	–
	16. Function series	János Kristóf		CSc	assoc. prof.	FT	Y	Y	18/18/18
	17. Functional analysis II	Zoltán Sebestyén		DSc	full prof.	FT	Y	Y	6/10/10
	18. Discrete optimization	András Frank		DSc	full prof.	FT	Y	Y	21/21/21
	19. Continuous optimization	Tibor Illés		PhD	assoc. prof.	FT	Y	Y	16/18/20
	20. Algorithms I.	Zoltán Király		PhD	assoc. prof.	FT	Y	Y	16/21/21
		Vince Grolmusz		DSc	full prof.	FT	Y	Y	8/16/16
Tibor Jordán		DSc	assoc. prof.	FT	Y	Y	21/23/23
András Benczúr		PhD	sen. asst. prof.	O	Y	Y	3/3/3
21. Discrete mathematics		László Lovász		acad.	full prof.	FT	Y	Y	10/10/10
21. Discrete mathematics		Zoltán Király		PhD	assoc. prof.	FT	Y	Y	16/21/21

*Course names*	Lecturers
*Differentiated courses*	Lecturers (For each subject block the first name stands for the coordinator’s name)	Degree / title	Position	Type of employment	Giving lectures	Giving tutorials Y/N	Total credit value of BSc and MSc courses coordinated by the lecturer: in this program / in this institution / in Hungary
MSc in mathematics
1. Topics in group theory	Péter Pál Pálfy	acad.	full prof.	O	Y	Y	11/22/22
	Piroska Csörgő	CSc	assoc. prof.	FT	N	Y	–
	Péter Hermann	CSc	assoc. prof.	FT	Y	Y	–
	József Pelikán	dr. univ.	sen. asst. prof.	FT	Y	Y	6/6/6
	Csaba Szabó	DSc	assoc. prof.	FT	Y	Y	–
2. Topics in ring theory	István Ágoston	CSc	assoc. prof.	FT	Y	Y	11/11/11
	Emil Kiss	DSc	full prof.	FT	Y	Y	9/23/23
	József Pelikán	dr. univ.	sen. asst. prof.	FT	Y	Y	6/6/6
3. Commutative algebra	József Pelikán	dr. univ.	sen. asst. prof.	FT	Y	Y	6/6/6
	István Ágoston	CSc	assoc. prof.	FT	Y	Y	11/11/11
	Gyula Károlyi	CSc	assoc. prof.	FT	N	Y	0/4/4
4. Universal algebra and lattice theory	Emil Kiss	DSc	full prof.	FT	Y	Y	9/23/23
	Péter Pál Pálfy	acad.	full prof.	O	Y	Y	11/22/22
	Csaba Szabó	DSc	assoc. prof.	FT	Y	Y	–
5. Current topics in algebra	Emil Kiss	DSc	full prof.	FT	Y	Y	9/23/23
	István Ágoston	CSc	assoc. prof.	FT	Y	Y	11/11/11
	Piroska Csörgő	CSc	assoc. prof.	FT	N	Y	–
	Péter Hermann	CSc	assoc. prof.	FT	Y	Y	–
	Péter Pál Pálfy	acad.	full prof.	O	Y	Y	11/22/22
	József Pelikán	dr. univ.	sen. asst. prof.	FT	Y	Y	6/6/6
	Csaba Szabó	DSc	assoc. prof.	FT	Y	Y	–
6. Combinatorial number theory	András Sárközy	acad.	full prof.	FT	Y	Y	6/16/16
	Róbert Freud	CSc	assoc. prof.	FT	Y	Y	0/8/8
	Gyula Károlyi	CSc	assoc. prof.	FT	N	Y	0/4/4
7. Exponential sums in number theory	András Sárközy	acad.	full prof.	FT	Y	Y	6/16/16
7. Exponential sums in number theory	Gyula Károlyi	CSc	assoc. prof.	FT	N	Y	0/4/4
8. Multiplicative number theory	Mihály Szalay	CSc	assoc. prof.	FT	Y	Y	3/7/7
8. Multiplicative number theory	Gyula Károlyi	CSc	assoc. prof.	FT	N	Y	0/4/4
9. Topological vector spaces and Banach algebras	János Kristóf	CSc	assoc. prof.	FT	Y	Y	18/18/18
10. Representations of Banach-*-algebras and abstract harmonic analysis	János Kristóf	CSc	assoc. prof.	FT	Y	Y	18/18/18
11. Nonlinear functional analysis and its applications	János Karátson	PhD	assoc. prof.	FT	Y	Y	7/20/20
12. Operator semigroups	András Bátkai	PhD	sen. asst. prof.	FT	Y	Y	6/11/11
13. Unbounded operators of Hilbert spaces	Zoltán Sebestyén	DSc	full prof.	FT	Y	Y	6/10/10
14. Descriptive set theory	Miklós Laczkovich	acad.	full prof.	FT	Y	Y	7/22/22
15. Geometric foundations of 3D graphics	György Kiss	PhD	assoc. prof.	FT	Y	Y	13/18/18
16. Geometric modelling	László Verhóczki	PhD	assoc. prof.	FT	Y	Y	12/24/24
17. Geometric measure theory	Tamás Keleti	PhD	assoc. prof.	FT	Y	Y	7/16/16
17. Geometric measure theory	Zoltán Buczolich	CSc	assoc. prof.	FT	Y	Y	9/19/19
18. Complex manifolds	Róbert Szőke	CSc	assoc. prof.	FT	Y	Y	13/20/20
18. Complex manifolds	Árpád Tóth	PhD	assoc. prof.	FT	Y	Y	5/5/5
19. Chapters of complex function theory	Gábor Halász	acad.	full prof.	FT	Y	Y	13/24/24
	Róbert Szőke	CSc	assoc. prof.	FT	Y	Y	13/20/20
	Árpád Tóth	PhD	assoc. prof.	FT	Y	Y	5/5/5
20. Riemann surfaces	Róbert Szőke	CSc	assoc. prof.	FT	Y	Y	13/20/20
	Gábor Halász	acad.	full prof.	FT	Y	Y	13/24/24
	Árpád Tóth	PhD	assoc. prof.	FT	Y	Y	5/5/5
	István Sigray	PhD	lecturer	FT	Y	Y	3/3/3
21. Special functions	Gábor Halász	acad.	full prof.	FT	Y	Y	13/24/24
21. Special functions	István Sigray	PhD	lecturer	FT	Y	Y	3/3/3
22. Seminar in complex analysis	Róbert Szőke	CSc	assoc. prof.	FT	Y	Y	13/20/20
23. Riemannian geometry	Balázs Csikós	CSc	assoc. prof.	FT	Y	Y	9/25/25
	László Verhóczki	PhD	assoc. prof.	FT	Y	Y	12/24/24
	Gábor Moussong	PhD	sen. asst. prof.	FT	Y	Y	5/5/5
	Róbert Szőke	CSc	assoc. prof.	FT	Y	Y	13/20/20
	Gyula Lakos	PhD	asst. prof.	FT	N	Y	–
24. Lie groups and symmetric spaces	László Verhóczki	PhD	assoc. prof.	FT	Y	Y	12/24/24
	Balázs Csikós	CSc	assoc. prof.	FT	Y	Y	9/25/25
	Gábor Moussong	PhD	sen. asst. prof.	FT	Y	Y	5/5/5
	Róbert Szőke	CSc	assoc. prof.	FT	Y	Y	13/20/20
	Gyula Lakos	PhD	asst. prof.	FT	N	Y	–
25. Convex geometry	Károly Böröczky Jr	DSc	assoc. prof.	O	Y	Y	11/11/11
	Károly Bezdek	DSc	full prof.	FT	Y	Y	7/12/12
	Gábor Kertész	dr. univ	sen. asst. prof.	FT	Y	Y	–
26. Discrete geometry	Károly Bezdek	DSc	full prof.	FT	Y	Y	7/12/12
	Károly Böröczky Jr	DSc	assoc. prof.	O	Y	Y	11/11/11
	Gábor Kertész	dr. univ	sen. asst. prof.	FT	Y	Y	–
27. Finite geometries	György Kiss	PhD	assoc. prof.	FT	Y	Y	13/18/18
	Tamás Szőnyi	DSc	full prof.	FT	Y	Y	9/9/9
	Péter Sziklai	CSc	assoc. prof.	FT	Y	Y	0/9/9
28. Differential topology problem solving	András Szűcs	acad	full prof.	FT	Y	N	16/22/22
	Balázs Csikós	CSc	assoc. prof.	FT	Y	Y	9/25/25
	László Fehér	PhD	sen. asst. prof.	FT	Y	Y	–
	Gyula Lakos	PhD	asst. prof.	FT	N	Y	–
	Gábor Lippner		res. fellow	O	N	Y	–
	Gábor Moussong	PhD	sen. asst. prof.	FT	Y	Y	5/5/5
	Endre Szabó	PhD	res. fellow	O	N	Y	–
	Árpád Tóth	PhD	assoc. prof.	FT	Y	Y	5/5/5
29. Algebraic and differential topology	András Szűcs	acad	full prof.	FT	Y	N	16/22/22
	Balázs Csikós	CSc	assoc. prof.	FT	Y	Y	9/25/25
	László Fehér	PhD	sen. asst. prof.	FT	Y	Y	–
	Gábor Moussong	PhD	sen. asst. prof.	FT	Y	Y	5/5/5
	András Némethi	DSc	sci. advisor	O	Y	Y	3/3/3
	András Stipsicz	DSc	sen. res. fellow	O	Y	Y	3/3/3
	Árpád Tóth	PhD	assoc. prof.	FT	Y	Y	5/5/5
30. Supplementary chapters of topology I. – Topology of singularities.	András Némethi (András Szűcs)	DSc	sci. advisor	O	Y	Y	3/3/3
	Balázs Csikós	CSc	assoc. prof.	FT	Y	Y	9/25/25
	László Fehér	PhD	sen. asst. prof.	FT	Y	Y	–
	Gábor Moussong	PhD	sen. asst. prof.	FT	Y	Y	5/5/5
	András Stipsicz	DSc	sen. res. fellow	O	Y	Y	3/3/3
	Árpád Tóth	PhD	assoc. prof.	FT	Y	Y	5/5/5
31. Supplementary Chapters of Topology II Low dimensional manifolds	András Stipsicz (András Szűcs)	DSc	sen. res. fellow	O	Y	Y	3/3/3
	Balázs Csikós	CSc	assoc. prof.	FT	Y	Y	9/25/25
	László Fehér	PhD	sen. asst. prof.	FT	Y	Y	–
	Gábor Moussong	PhD	sen. asst. prof.	FT	Y	Y	5/5/5
	András Némethi	DSc	sci. advisor	O	Y	Y	3/3/3
	Árpád Tóth	PhD	assoc. prof.	FT	Y	Y	5/5/5
32. Set theory I	Péter Komjáth	DSc	full prof.	FT	Y	N	12/20/20
33. Set theory II	Péter Komjáth	DSc	full prof.	FT	Y	N	12/20/20
34. Complexity theory	Vince Grolmusz	DSc	full prof.	FT	Y	Y	8/16/16
	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
	László Lovász	acad.	full prof.	FT	Y	Y	10/10/10
35. Applied discrete mathematics seminar	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
36. Geometric algorithms	Katalin Vesztergombi	CSc	assoc. prof.	FT	Y	Y	3/3/3
37. Selected topics in graph theory	László Lovász	acad.	full prof.	FT	Y	Y	10/10/10
37. Selected topics in graph theory	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
38. Graph theory seminar	László Lovász	acad.	full prof.	FT	Y	Y	10/10/10
39. Intorduction to information theory	István Szabó	CSc.	assoc prof.	O	Y	N	6/9/9
40. Stochastic processes with independent increment, limit theorems	Vilmos Prokaj	PhD	assoc. prof..	FT	Y	N	5/23/23
41. Analysis of time series	László Márkus	CSc	assoc. prof.	FT	Y	Y	6/22/22
42. Cryptography	István Szabó	CSc	assoc. prof.	O	Y	N	3/6/6
43. Statistical hypotheses testing	Villő Csiszár		asst. prof.	FT	Y	N	3/3/3
44. Statistical computing 2	András Zempléni	CSc	assoc. prof.	FT	Y	Y	6/24/24
45. Discrete mathematics II	Tamás Szőnyi	DSc	full prof.	FT	Y	Y	9/9/9
	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
	László Lovász	acad.	full prof.	FT	Y	Y	10/10/10
46. Dynamical systems and differential equations	Péter Simon	PhD	assoc. prof.	FT	Y	Y	9/22/22
47. Partial differential equations	László Simon	DSc	full prof.	FT	Y	Y	9/25/25
48. Dynamical systems	Zoltán Buczolich	CSc	assoc. prof.	FT	Y	Y	9/19/19
49. Discrete dynamical systems	Zoltán Buczolich	CSc	assoc. prof.	FT	Y	Y	9/19/19
50. Ergodic theory	Zoltán Buczolich	CSc	assoc. prof.	FT	Y	Y	9/19/19
51. Dynamics in one complex variable	István Sigray	PhD	Lecturer	FT	Y		3/3/3
52. Approximation algorithms	Tibor Jordán	DSc	assoc. prof.	FT	Y	Y	21/23/23
53. Applications of operation reserach	Gergely Mádi-Nagy	PhD	sen. asst. prof.	FT	Y	Y	15/12/21
54. Investment analysis	Róbert Fullér	CSc	assoc. prof.	FT	Y	Y	15/21/24
55. Integer Programming I.	Tamás Király	PhD	sen. asst. prof.	FT	Y	Y	12/18/18
56. Integer Programming II.	Tamás Király	PhD	sen. asst. prof.	FT	Y	Y	12/18/18
57. Graph theory	András Frank	DSc	full prof.	FT	Y	Y	21/21/21
57. Graph theory	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
58. Graph theory tutorial	András Frank	DSc	full prof.	FT	Y	Y	21/21/21
58. Graph theory tutorial	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
59.Game theory	Tibor Illés	PhD	assoc. prof.	FT	Y	Y	16/18/20
60. Inventory management	Gergely Mádi-Nagy	PhD	assoc. prof.	FT	Y	Y	15/21/21
61. Combinatorial algorithms I.	Tibor Jordán	DSc	assoc. prof.	FT	Y	Y	21/23/23
62. Combinatorial algorithms II	Tibor Jordán	DSc	assoc. prof.	FT	Y	Y	21/23/23
63. Structures in combinatorial optimization	Tibor Jordán	DSc	full prof.	FT	Y	Y	21/23/23
64. Combinatorial structures and algorithms	Tibor Jordán	DSc	assoc. prof.	FT	Y	Y	21/23/23
65. LEMON library: solving optimization problems in C++	Alpár Jüttner		asst. prof.	O	N	Y	3/3/3
66. Linear optimization	Tibor Illés	PhD	assoc. prof.	FT	Y	Y	16/18/20
67. Matroid theory	András Frank	DSc	full prof.	FT	Y	Y	21/21/21
68. Macroeconomy and the theory of economic equilibrium	Gergely Mádi-Nagy	PhD	sen. asst. prof.	O	Y	Y	15/21/21
68. Microeconomy	Gergely Mádi-Nagy	PhD	sen. asst. prof.	O	Y	Y	15/21/21
69. Nonlinear optimization	Tibor Illés	PhD	assoc. prof.	FT	Y	Y	16/18/20
70. Computational methods in operations research	Gergely Mádi-Nagy	PhD	sen. asst. prof.	FT	Y	Y	15/21/21
71. Operations research project	Róbert Fullér	CSc	assoc. prof.	FT	Y	Y	15/21/24
72. Market analysis	Róbert Fullér	CSc	assoc. prof.	FT	Y	Y	15/21/24
73. Polyhedral combinatorics	Tamás Király	PhD	sen. asst. prof.	FT	Y	Y	12/18/18
74. Stochastic optimization	Csaba Fábián	PhD	sen. asst. prof.	O	Y	Y	6/19/25
75. Stochastic optimization practice	Csaba Fábián	PhD	sen. asst. prof.	O	Y	Y	6/19/25
76. Manufacturing process management	Tamás Király	PhD	sen. asst. prof.	FT	Y	Y	12/18/18
77. Multiple objective optimization	Fullér Róbert	CSc	assoc. prof.	FT	Y	Y	15/21/24
78. Scheduling theory	Tibor Jordán	CSc	assoc. prof.	FT	Y	Y	21/23/23
79. Business economics	Róbert Fullér	CSc	assoc. prof.	FT	Y	Y	15/21/24
80. Optional subject		N/A
81. Data mining	András Lukács	CSc	sen. res. fellow.	O	Y	Y	6/6/6
82. Mathematics of networks and the WWW	András Benczúr	PhD	sen. asst. prof.	O	Y	Y	3/3/3
83. Complexity theory seminar	Vince Grolmusz	DSc	full prof.	FT	Y	Y	8/16/16
	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
	László Lovász	acad.	full prof.	FT	Y	Y	10/10/10
84. Design, analysis and implementation of algorithms and data structures I	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
	András Benczúr	PhD	sen. asst. prof.	O	Y	Y	3/3/3
	Tibor Jordán	DSc	assoc. prof.	FT	Y	Y	21/23/23
85. Design, analysis and implementation of algorithms and data structures II	Zoltán Király	PhD	assoc. prof.	FT	Y	Y	16/21/21
86. Codes and symmetric structures	Tamás Szőnyi	DSc	full prof.	FT	Y	Y	9/9/9
86. Codes and symmetric structures	Péter Sziklai	CSc	assoc. prof.	FT	Y	Y	0/9/9

MSc in Mathematics: Personal data

Name: István Ágoston

Date of birth: 1959

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi professor's scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Eötvös University (1984– ):

algebra (for students in mathematics; lecture, practice)

algebra and number theory (for students in teaching mathematics; lecture, practice)

linear algebra (for students in informatics; lecture, practice)

analysis (for students in teaching mathematics; lecture, practice)

ring theory, homological algebra, Lie algebras, representation theory (for students in mathematics; lecture)

Carleton University, Ottawa (1986–1991, 1996, 2002, 2004)

linear algebra (general audience; lecture, practice)

calculus, analysis, complex functions, combinatorics, abstract algebra, numerical analysis, linear programming, matheatical logic, formal languages and automata theory (general audience and honours students in mathematics; practice)

University of Ottawa(2002)

group theory (students in mathematics; lecture, practice)

BSM (1997, 1998)

basic algebra (students in mathematics; lecture, practice)

group representations (students in mathematics; lecture, practice)

Other professional activity:

25 years of teaching experience, 3 diploma thesis supervisions, 1 Ph.D. thesis supervision

20 papers with over 100 citations

over 25 lectures at international conferences and seminars

Up to 5 selected publications from the past 5 years:

1. Ágoston, I., Dlab, V., Lukács, E.: Quasi-hereditary extension algebras, Algebras and Representation theory 6 (2003), 97–117.

2. Ágoston, I., Dlab, V., Lukács, E.: Standardly stratified extension algebras, Comm. Alg. 33 (2005), 1357–1368.

3. Ágoston, I., Dlab, V., Lukács, E.:: Approximations of algebras by standardly stratified algebras, Journal of Algebra 319 (2008), 4177–4198.

The five most important publications:

1. Ágoston, I., Dlab, V., Lukács, E.: Homological duality and quasi-heredity, Canadian Journal of Mathematics 48 (1996), 897–917.

2. Ágoston, I., Lukács, E., Ringel, C.M.: Realizations of Frobenius functions, Journal of Algebra 210 (1998), 419–439.

3. Ágoston, I., Happel, D., Lukács E., Unger, L.: Finitistic dimension of standardly stratified algebras, Comm. Alg., 28(6) (2000) 2745–2752.

4. Ágoston, I., Happel, D., Lukács E., Unger, L.: Standardly stratified algebras and tilting, J. of Algebra, 226 (2000) 144–160.

5. Ágoston, I., Dlab, V., Lukács, E.: Quasi-hereditary extension algebras, Algebras and Representation theory 6 (2003), 97–117.

Activity in the scientific community, international relations

Periodica Mathematica Hungarica (managing editor, 1994–1997)

organizer of international conferences in algebra (1992, 1996, 1999, 2001);

leader of German–Hungarian cooperation projects (1998–1999, 2001–2003)

member of the granting committee of the Hungarian NSRF (OTKA), 2000–2002

local coordinator of a CEEPUS project (2003–2005)

leader of a Canadian–Hungarian cooperation project (2004–2006)

OTKA project leader (2007–2011)

long term visits in Canada (altogether 26 months), Germany (2,5 months)

coauthors from Canada, Germany and Japan

Name: Miklós Arató

Date of birth: 1962

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1985– ):

probability theory (for students in applied mathematics, informatics; lecture, practice)

probability theory (for students in mathematics; practice)

statistics (for students in informatics; lecture, practice)

statistics (for students in mathematics, applied mathematics; practice)

multivariate statistics (for students in mathematics, applied mathematics; lecture, practice)

premium calculation (for students in mathematics, applied mathematics; lecture, practice)

financial processes (for students in mathematics, applied mathematics; lecture, practice)

risk processes (for students in mathematics, applied mathematics; lecture, practice)

Other professional activity:

23 years of teaching experience, 22 diploma thesis supervisions, 1 Ph.D. thesis supervisions;

over 15 lectures at international conferences;

19 publications;

Up to 5 selected publications from the past 5 years:

1. N.M. Arató, D. Bozsó, P. Elek and A. Zempléni: Forecasting and Simulating Mortality Tables, Mathematical and Computer Modelling (2008)

2. T. Faluközy, I. I. Vitéz and N. M. Arató: Stochastic models for claims reserving in insurance business, RECENT ADVANCES IN STOCHASTIC MODELING AND DATA ANALYSIS (2007)

3. Miklós Arató: Will there be annuities from voluntary pension funds?, Economic Review (2006)

4. Miklós Arató: Who shall we bow out of the pension funds?, Economic Review (2006)

5. N. M. Arató, I. L. Dryden and C. C. Taylor: Hierarchical Bayesian modelling of spatial age-dependent mortality, Computational Statistics & Data Analysis (2006)

The five most important publications:

1. N.M. Arató: On a limit theorem for generalized Gaussian random fields corresponding to stochastic partial differential equations, Probability Theory and Applic. (1989)

2. N.M. Arató: Equivalence of Gaussian measures corresponding to generalized Gaussian random fields, Appl. Math. Lett. (1989)

3. N.M. Arató: The estimate of potential in stochastic Schrödinger's equation, Computers Math. Applic. (1995)

4. N.M. Arató: Mean estimation of Brownian and Ornstein-Uhlenbeck Sheets, Probability Theory and Applic. (1997)

5. N.M. Arató: On the estimation of the mean value of Levy's Brownian motion, Probability Theory and Applic. (1998)

Activity in the scientific community, international relations

president of the Hungarian Actuarial Society, 2003-2007;

member of the Board of the Hungarian Actuarial Society, 1995-;

member of the International Bernoully Society, 1990–;

Name: András Bátkai

Date of birth: 1972

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Bolyai scholarship (2004–2007)

Teaching activity (with list of courses taught so far):

Eötvös University (2000– ):

analysis (for students in mathematics; lecture, practice)

calculus (for students in biology; practice)

special corses for PhD students

Other professional activity:

Over 10 years of teaching experience, 5 diploma thesis supervisions;

over 20 lectures at international conferences;

Three organized conferences

17 research articles and one monograph;

Up to 5 selected publications from the past 5 years:

1. A.B., Schnaubelt, R., Asymptotic behaviour of parabolic problems with delays in the highest order derivatives, Semigroup Forum 69(2004), 369-399.

2. A.B., K.J. Engel, "Abstract wave equations with generalized Wentzell boundary conditions", J. Diff. Eqs. 207 (2004), 1-20.

3. Spectral problems for operator matrices (with P. Binding, A. Dijksma, R. Hryniv and H. Langer), Math. Nachr. 278 (2005), 1408-1429.

4. Polynomial stability of operator semigroups (with K.J. Engel, J. Prüss and R. Schnaubelt), Math. Nachr. 279 (2006), 1425-1440.

5. Cosine families generated by second order differential operators on W^1,1(0,1) with generalized Wentzell boundary conditions (with K.J. Engel and M. Haase), Applicable Analysis 84 (2005), 867-876.

The five most important publications:

1. Semigroups for delay equations (with S. Piazzera), monograph, A. K. Peters: Wellesley MA, Research Notes in Mathematics vol. 10, ISBN: 1-56881-243-4, 2005.

2. Bátkai, A., Piazzera, S., „Semigroups and linear partial differential equations with delay”, J. Math. Anal. Appl. 64(2001), 1-20.

3. Bátkai, A., Fasanga, E., Shvidkoy, R., „Hyperbolicity of delay equations via Fourier multipliers”, Acta Sci. Math (Szeged) 69(2003), 131-145.

4. Bátkai, A., „Hyperbolicity of linear partial differential equations with delay”, Integral Eq. Oper. Th. 44(2002), 383-396.

5. Bátkai, A., Piazzera, S., „A semigroup method for delay equations with relatively bounded operators in the delay term”, Semigroup Forum 64(2002), 71-89.

Activity in the scientific community, international relations

Marie Curie Postdoctoral Fellowships in Vienna and Rome;

„Farkas Gyula” and „Alexits György” prize;

coauthors from Germany, Italy, USA, France;

Alexander von Humboldt fellowship;

Name: András A. Benczúr

Date of birth: 1969

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant professor (part time) and

Computer and Automation Institute, Hungarian Academy of Sciences (full time)

Scientific degree (discipline): PhD (applied mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1997– ):

Theory of algorithms, in English and in Hungarian;

Advanced algorithms for Data Mining, Data Streams and the World Wide Web, graduate courses.

Central European University:

Statistics, in English

Other professional activity:

Over 10 years of teaching experience, over 15 lectures at international conferences

Project coordinator in a number of R&D project concerning text mining, personalization and similarity search technologies, network data mining, approximate counting of very large data streams, efficient algorithms for massive data

Up to 5 selected publications from the past 5 years:

1. To Randomize or Not To Randomize: Space Optimal Summaries for Hyperlink Analysis. In Proc. of 15th WWW Conference, 2006. (Joint with T. Sarlós, K. Csalogány, D. Fogaras and B. Rácz.)

2 SpamRank: Fully automatic link spam detection, Proc. Airweb 2005. (Joint with Károly Csalogány, Tamás Sarlós and Máté Uher), to appear in Information Retrieval.

3. Primal-dual approach for directed vertex connectivity augmentation and generalizations
Proc 16th ACM-SIAM Symp. on Discrete Algorithms, pp. 500-509, 2005. (Joint with László A.Végh). Transactions on Algorithms, to appear.

4. A. A. Benczúr, K. Csalogány, T. Sarlós: Similarity Search to Fight Web Spam. In Proc. Airweb 2006 in conjunction with SIGIR 2006.

The five most important publications:

1. To Randomize or Not To Randomize: Space Optimal Summaries for Hyperlink Analysis. In Proc. of 15th WWW Conference, 2006. (Joint with T. Sarlós, K. Csalogány, D. Fogaras and B. Rácz.)

2 SpamRank: Fully automatic link spam detection, Proc. Airweb 2005. (Joint with Károly Csalogány, Tamás Sarlós and Máté Uher), to appear in Information Retrieval.

4. A. A. Benczúr, K. Csalogány, T. Sarlós: Similarity Search to Fight Web Spam. In Proc. Airweb 2006 in conjunction with SIGIR 2006.

5. Approximating s-t minimum cuts in O(n²) time, J. Alg 37(1): 2-36, 2000. (Joint with David R. Karger)

Activity in the scientific community, international relations

Name: Károly Bezdek

Date of birth: 1955

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, professor

Scientific degree (discipline): Doctor of Science (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1998–2001)

Teaching activity (with list of courses taught so far):

Eötvös University (1978– ):

Geometry (all levels), various topics in convex and discrete geometry (for students in mathematics; lecture, practice)

University of Calgary (2004–)

Transformation Geometry, Differential Geometry, Geometry, Discrete Geometry, Convex Polytopes, Convexity, Analytic Convexity – Higher Dimensions

Other professional activity:

30 years of teaching experience, 10 diploma thesis supervisions, 4 Ph.D. thesis supervisions;

over 20 lectures at international conferences;

97 publications;

Up to 5 selected publications from the past 5 years:

1. Bezdek, K., Lángi, Zs., Naszódi, M., and Papez, P.: Ball-Polyhedra, Discrete Comput.

Geom. 38(2) (2007), 201-230.

2. Bezdek, K., and Litvak, A.: On the vertex index of convex bodies, Advances in

Mathematics 215(2) (2007), 626-641.

3. Bezdek, K., Naszódi, M., and Oliveros-Braniff, D.: Antipodality in hyperbolic space,

Journal of Geometry, 85 (2006), 22-31.

4. Bezdek, K.: On the monotonicity of the volume of hyperbolic convex polyhedra, Beiträge

zur Algebra und Geometrie. Contributions to Algebra and Geometry 46(2) (2005), 609-

614.

5. Bezdek, K., and Daróczy-Kiss, E.: Finding the best face on a Voronoi polyhedron – the

strong dodecahedral conjecture revisited, Monatshefte für Mathematik, 145 (2005), 191-

206.

The five most important publications:

1. Bezdek, K.: Circle-packings into convex domains of the Euclidean and hyperbolic plane
and the sphere, Geometriae Dedicata, 21 (1986), 249-255.

2. Bezdek, K., and Connelly, R.: Covering curves by translates of a convex set, Amer. Math.
Monthly 96/9 (1989), 789-806.

3. Bezdek, K.: The problem of illumination of the boundary of a convex body by affine
subspaces, Mathematika 38 (1991), 362-375.

4. Bezdek, K.: Improving Rogers’ upper bound for the density of unit ball packings via
estimating the surface area of Voronoi cells from below in Euclidean d−space for
all d ≥ 8, Discrete Comput. Geom. 28 (2002), 75-106.

5. Bezdek, K., and Connelly, R.: Pushing disks apart - the Kneser-Poulsen conjecture
in the plane, J. reine angew. Math. 553 (2002), 221-236.

Activity in the scientific community, international relations

Editor in chief of the journal Contribution to Discrete Mathematics, 2006– ;

Organizer of several international conferences;

Coauthors from USA, Canada, England, Germany, Mexico;

Invited speaker at international conferences and workshops more than 100 times;

Visiting professor at

– Cornell University, New York, USA;

– University of Texas at Austin, Texas, USA;

– University of Calgary, Calgary, Kanada .

Name: Károly Böröczky, Jr.

Date of birth: 1964

Highest degree (discipline): diploma in mathematics

Present employer, position: Rényi Institute, Eötvös University, associate professor

Scientific degree (discipline): Doctor of Science (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1998–2001), Bolyai Scholarship (2001-2004, 2005-2008)

Teaching activity (with list of courses taught so far):

Eötvös University (1994– ):

Geometry (for students in mathematics; lecture, practice)

BSM (1994– ):

Complex functions, Algebraic Topology, Topics in Analysis (lecture, practice)

Other professional activity:

1 diploma thesis supervisions, 1 Ph.D. thesis supervision;

over 20 lectures at international conferences;

60 publications;

Up to 5 selected publications from the past 5 years:

1. K. Böröczky, Jr.: Finite packing and covering, Cambridge University Press, 2004.

2. K. Böröczky, Jr.: The stability of the Rogers-Shepard inequality, Adv. Math.,

190 (2005), 47-76.

3. K. Böröczky, Jr.: Finite packing and covering by congruent convex domains. Disc. Comp. Geom., 30 (2003), 185-193.

4. K. Böröczky, Jr., M. Reitzner: Approximation of Smooth Convex Bodies by Random Circumscribed Polytopes. Annals of Applied Prob., 14 (2004), 239-273.

5. K. Böröczky, Jr.: Finite coverings in the hyperbolic plane.

Discrete and Computational Geometry, 33 (2005), 165-180.

The five most important publications:

1. K. Böröczky, Jr.: Finite packing and covering, Cambridge University Press, 2004.

2. K. Böröczky, Jr.: The stability of the Rogers-Shepard inequality, Adv. Math.,
190 (2005), 47-76.

3. K. Böröczky, Jr.: Approximation of general smooth convex bodies. Adv. Math.,
153 (2000), 325-341.

4. K. Böröczky, Jr.: Finite coverings in the hyperbolic plane. Discrete and Computational

Geometry, 33 (2005), 165-180.

5. K. Böröczky, Jr.: About four-ball packings, Mathematika, 40 (1993), 226-232.

Activity in the scientific community, international relations

organizer of seven international conferences;

visiting professor at universities in Germany, England, USA;

coordinator of various Hungarian and EU grants

Name: Zoltán Buczolich

Date of birth: 1961

Highest degree (discipline): diploma in Mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): D. Sc. (mathematics), + habilitation at the Eötvös University

Major Hungarian scholarships: Széchenyi Professor scholarship (1997–2001),

Öveges Professor scholarship (2006-2007)

Teaching activity (with list of courses taught so far):

Eötvös University (1985– ):

analysis (8 different couses for students in mathematics education + B. Sc. Medium level mathematics; lecture, practice)

Discrete Dynamical systems (for students in mathematics, applied mathematics, graduate school; lecture)

Chapters in Dynamical Systems (for students in mathematics, applied mathematics, graduate school; lecture)

Ergodic Theory (for students in mathematics, applied mathematics, graduate school; lecture)

Complex Funcions (for students in Mathematics, practice)

Budepest Semesters in mathematics (1990–96 ):

Complex Functions (lecture, practice)

University of California Davis, (1989-1990): Calculus, Differential Equations, Harmonic Analysis.

University of Wisconsin, Milwaukee (1994): Calculus and Introduction to Fractal Geometry.

Michigan State University, (2001-2002): Calculus, Analysis, Honors Analysis.

University of North Texas, (2003): Business Calculus.

Other professional activity:

23 years of continuous teaching experience, 13 diploma thesis supervisions, 2 student research paper supervisions, over 50 lectures at international conferences; over 30 lectures at departmental seminars of foreign universities, 72 publications;

Up to 5 selected publications from the past 5 years:

1. Z. Buczolich and C. E. Weil, Infinite Peano Derivatives, extensions, and the Baire one property, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia (2004), no. 1, 117--149 (2005).

2. I. Assani, Z. Buczolich and D. Mauldin, An L^1 Counting problem in Ergodic Theory, J. Anal. Math. {\bf 95} (2005), 221--241.

3. Z. Buczolich and U. B. Darji, Pseudoarcs, Pseudocircles, Lakes of Wada and Generic Maps on S^2, Topology Appl. 150 (2005), no. 1-3, 223--254.

4. Z. Buczolich, Solution to the gradient problem of C. E. Weil, Rev. Mat. Iberoamericana, 21 (2005) No. 3., 889-910.

5. Z. Buczolich, Universally L^1 good sequences with gaps tending to infinity, Acta Math. Hungar., 117 (1-2) (2007), 91-40.

The five most important publications:

[1] Z. Buczolich, A general Riemann complete integral in the plane, Acta Math. Hungar. 57 (1991), no. 3-4, 315–323.

[2] Z. Buczolich, Density points and bi-Lipschitz functions in Rm, Proc. Amer. Math. Soc. 116 (1992), no. 1, 53–59.

[3] Z. Buczolich, Arithmetic averages of rotations of measurable functions, Ergodic Theory Dynam. Systems 16 (1996), no. 6, 1185–1196.

[4] Z. Buczolich, Solution to the gradient problem of C. E. Weil, Rev. Mat. Iberoamericana, 21 (2005) No. 3., 889-910.

[5] I. Assani, Z. Buczolich and D. Mauldin, An L1 Counting problem in Ergodic Theory, J. Anal. Math. 95 (2005), 221–241.

Activity in the scientific community, international relations

Real Analysis Exchange (editor), 2004– ;

organizer of three international conferences and a Summer School;

secretary of the Scientific commitee of the Bolyai Mathematical Society (1990-93);

member of the Mathematical commitee of the Hungarian Academy of Sciences (1994-96);

member of the granting committee of the Hungarian NSRF (OTKA), 1996–2000;

coauthors from USA, Poland, France, Belgium;

visiting professor at universities in USA;

member of the Hungarian and the American Mathematical Society.

Name: Balázs Csikós

Date of birth: 1959

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Eötvös University (1988– ):

Lie Groups, Algebraic Curves (for PhD students in mathematics; lectures)

Geometry, Algebraic Topology, Differential Geometry, Theory of Bundles and Connections, General Differential Geometric Structures (for students in mathematics; lectures and practices)

Geometric Foundations of 3D graphics (for students in applied mathematics; computer lab practice)

BSM (1990– ):

Topics in Geometry, Algebraic Topology, Differential Topology, Differential Geometry.

(lectures)

CEU (2002– ):

Differential Geometry, Lie Groups (for PhD students, lectures)

Other professional activity:

20 years of teaching experience, 12 diploma thesis supervisions, 2 Ph.D. thesis supervisions;

over 26 lectures at international conferences;

28 publications;

Up to 5 selected publications from the past 5 years:

1. Bezdek, K., Connelly, R., and Csikós, B.: On the perimeter of the intersection of congruent disks. Beiträge zur Algebra und Geometrie, 47(1) (2006), 53-62.

2. Bezdek, K., Bisztriczky, T., Csikós, B., and Heppes, A.: On the transversal Helly numbers of disjoint and overlapping disks, Archiv der Math., 87(1) (2006), 86-96.

3. Csikós, B., and Moussong, G.: On the Kneser-Poulsen Conjecture in Elliptic Space. Manuscripta Math., 121(4) (2006), 481-489.

4. Csikós, B., Lángi, Zs., and Naszódi, M.: A generalization of the discrete isoperimetric inequality for piecewise smooth curves of constant geodesic curvature, Periodica Math. Hung., 53(1-2) (2006), 121-132.

5. Csikós, B., Németh, B., and Verhóczki, L.: Volumes of principal orbits of isotropy subgroups in compact symmetric spaces, Houston Journal of Math., 33(3) (2007), 719-734.

The five most important publications:

1. Csikós, B.: On the volume of the union of balls, Discrete Comput. Geom., 20 (1998), 449-461.

2. Csikós, B.: On the volume of flowers in space forms, Geometriae Dedicata, 86 (2001), 59-79.

3. Csikós, B.: A Schläfli-type formula for polytopes with curved faces and its application to the Kneser-Poulsen conjecture, Monatshefte für Mathematik, 147(4) (2006), 273-292.

4. Csikós, B.: On the Rigidity of Regular Bicycle (n,k)-gons. Contributions to Discrete Mathematics, 2(1) (2007). 94-107.

5. Csikós, B. and Verhóczki, L.: Classification of Frobenius Lie algebras of dimension ≤ 6. Publ. Math. Debrecen, 70(3-4) (2007), 427-451.

Activity in the scientific community, international relations

deputy director of the Institute of Mathematics (2006–) and head of the Department of Geometry (2008–) at Eötvös University;

organizer of 2 international conferences;

member of the granting committee of the Hungarian NSRF (OTKA), 1999–2006;

member of the Bolyai Mathematical Society;

coauthors from Canada, South Africa, USA;

visiting professor at universities in Hungary (CEU), Belgium, Canada;

Name: Villő Csiszár

Date of birth: 1975

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): -

Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):

Probability theory (for students in informatics and mathematics; lecture, practice)

Statistics (for students in informatics and mathematics; lecture, practice)

Information theory (for students in mathematics; lecture)

Markov chains (for students in mathematics; lecture)

Large deviations (for students in mathematics; lecture)

Other professional activity:

8 years of teaching experience, 2 diploma thesis supervisions.

Up to 5 selected publications from the past 5 years:

1. Csiszár, V., Móri, T. F.: The convexity method of proving moment-type inequalities. Statist. Probab. Lett.,66 (2004).

2. Csiszár, V., Móri, T. F., Székely, G. J.: Chebyshev-type inequalities for scale mixtures. Statist. Probab. Lett.,71 (2005).

3. Csiszár, V., Móri, T. F.: Sharp integral inequalities for products of convex functions. JIPAM J. Inequal. Pure Appl. Math. 8/4 (2007), Art. 94 (electronic).

4. Csiszár, V., Rejtő, L., Tusnády, G.: Statistical inference on random structures. In: Győri, E., Katona, G. O. H., Lovász, L. (eds.): Horizon of Combinatorics. Bolyai Society Mathematical Studies 17, Springer, Berlin (2008).

5. Csiszár, V.: Conditional independence relations and log-linear models for random matchings. Acta Math. Hungar. Online First (2008).

The five most important publications:

1. Makra, Horváth, Zempléni, Csiszár, Rózsa, Motika: Some characteristics of air quality parameters in Southern Hungary. EURASAP Newsletter 42 (2001).

2. Csiszár, V., Móri, T. F.: The convexity method of proving moment-type inequalities. Statist. Probab. Lett.,66 (2004).

3. Csiszár, V., Móri, T. F., Székely, G. J.: Chebyshev-type inequalities for scale mixtures. Statist. Probab. Lett.,71 (2005).

5. Csiszár, V.: Conditional independence relations and log-linear models for random matchings. Acta Math. Hungar. Online First (2008).

Activity in the scientific community, international relations:

Member of the Bolyai Mathematical Society

Name: Piroska Csörgő

Date of birth: 1950

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi István scholarship (2003–2006)

Teaching activity (with list of courses taught so far):

Eötvös University (1974– ):

algebra and number theory (for students in mathematics; lecture and practice)

linear algebra (for students in informatics; practice)

introduction to mathematics (for students in informatics, practice)

analysis (for students in mathematics; practice)

Other professional activity:

34 years of teaching experience, over 10 diploma thesis supervisisons, over 20 lectures at international conferences, 31 publications

Up to 5 selected publications from the past 5 years:

1. P. Csörgő, Abelian inner mappings and nilpotency class greater than two, European Journal of Combinatorics 28 (2007), 858–867.

2. P. Csörgő, On connected transversals to abelian subgroups and looptheoretical consequences, Archiv der Mathematik 47 (2005), 242–265.

3. P. Csörgő, A. Drápal, Left conjugacy closed loops of nilpotency class two, Resultate der Mathematik 47 (2005), 242–265.

4. M. Asaad, P. Csörgő, Characterization of finite groups with some S-quasinormal subgroups, Monatshefte für Mathematik, 146 (2005), 263–266.

5. P. Csörgő, M. Herzog, On supersolvable groups and the nilpotator, Communications in Algebra Vol. 32, No2. (2004), 609-620.

The five most important publications:

1. P. Csörgő, Abelian inner mappings and nilpotency class greater than two, European Journal of Combinatorics 28 (2007), 858–867.

2. P. Csörgő, On connected transversals to abelian subgroups and looptheoretical consequences, Archiv der Mathematik 47 (2005), 242–265.

3. P. Csörgő, M. Niemenmaa, On connected transversals to nonabelian subgroups, European Journal of Combinatorics 23 (2002), 179–185.

4. P. Csörgő, M. Niemenmaa, Solvability conditions for loops and groups, Journal of Algebra 232 (2000), 336–342.

5. M. Asaad, P. Csörgő, The influence of minimal subgroups on the structure of finite groups, Archiv der Mathematik 72 (1999), 401–404.

Activity in the scientific community, international relations

opponent of theses and membership in committees for PhD, CSc and DSc degrees

refereeing to many international journals

editor at Journal of Mathematical Sciences: Advances and Applications (2008– )

visiting professor at universities in Chicago and in Prague

coauthors from USA, Finland, Germany, Czech Republic, Israel and Egypt

Name: Csaba Fábián

Date of birth: 1958

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1992– ):

Operations research (for students in informatics; lecture, practice);

Stochastic programming, Simulation, OR methods in risk management (for students in mathematics; lecture);

OR software (for students in informatics; practice);

Linear programming methods and solvers (for students in mathematics; practice).

Organizer of Seminar in continuous optimization (for researchers and students in mathematics).

Other professional activity:

16 years of teaching experience,

over 10 diploma thesis supervisions, 3 Ph.D. thesis supervisions;

over 10 lectures at international conferences;

12 publications;

4 optimization packages with applications in transportation, chemistry, and military.

12 citations to above works.

Up to 5 selected publications from the past 5 years:

1. C.I. Fábián “Decomposing CVaR minimization in two-stage stochastic models”. Stochastic Programming E-Print Series 20-2005.

2. C.I. Fábián and Z. Szőke “Solving two-stage stochastic programming problems with level decomposition”. Computational Management Science 4 (2007), 313-353.

3. C.I. Fábián “Handling CVaR objectives and constraints in two-stage stochastic models”. European Journal of Operational Research 191 (2008) (special issue on Continuous Optimization in Industry, T. Illés, M. Lopez, J. Vörös, T. Terlaky, G-W. Weber, eds.), 888-911.

4. C.I. Fábián and A. Veszprémi “Algorithms for handling CVaR-constraints in dynamic stochastic programming models with applications to finance”. The Journal of Risk 10 (2008), 111-131.

5. C.I. Fábián, G. Mitra, and D. Roman “Processing Second-order Stochastic Dominance models using cutting-plane representations”. CARISMA Technical Report 75 (2008), Brunel University, West London.

The five most important publications:

1. C.I. Fábián “Bundle-type methods for inexact data”. Central European Journal of Operations Research 8 (2000) (special issue, T. Csendes and T. Rapcsák, eds.), 35-55.

2. C.I. Fábián, A. Prékopa, and O. Ruf-Fiedler “On a dual method for a specially structured linear programming problem”. Optimization Methods and Software 17 (2002), 445-492.

3. C.I. Fábián and Z. Szőke “Solving two-stage stochastic programming problems with level decomposition”. Computational Management Science 4 (2007), 313-353.

4. C.I. Fábián “Handling CVaR objectives and constraints in two-stage stochastic models”. European Journal of Operational Research 191 (2008) (special issue on Continuous Optimization in Industry, T. Illés, M. Lopez, J. Vörös, T. Terlaky, G-W. Weber, eds.), 888-911.

5. C.I. Fábián and A. Veszprémi “Algorithms for handling CVaR-constraints in dynamic stochastic programming models with applications to finance”. The Journal of Risk 10 (2008), 111-131.

Name: István Faragó

Date of birth: 1950

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (2001–2004)

Teaching activity (with list of courses taught so far):

Eötvös University (1977– ):

Applied analysis (for students in mathematics; lecture)

analysis (for students in meteorology; lecture, practice)

Differential equation (for students in earth sciences; lecture)

Other professional activity:

30 years of teaching experience, 15 diploma thesis supervisions, 5 Ph.D. thesis supervisions;

over 40 lectures at international conferences;

110 publications;.

Up to 5 selected publications from the past 5 years:

1. I. Faragó, C. Palencia, Sharpening the estimate of the stability bound in the maximum-norm of the Crank--Nicolson scheme for the one-dimensional heat equation, Appl. Numer. Math. 42 (2002) 133-140.

2. J. Bartholy, I. Faragó, A. Havasi, Splitting method and its application in air pollution modelling, Idöjárás, 105 (2001) 39-58.

3. M. Botchev, I. Faragó, A. Havasi, Testing weighted splitting schemes on a one-column transport-chemistry model, in: S. Margenov, J. Wasniewski, P. Yalamov eds; Large-Scale Scientific Computing, Lect. Notes Comp. Sci., 2907, Springer Verlag, 2004, 295-302.

4 A. Dorosenko, I. Faragó, Á. Havasi, V. Prussov, , On the numerical solution of the three-dimensional advection-diffusion equation, Problems in Programming, 7 (2006) 641-647.

5. P. Csomós, I. Faragó, Error analysis of the numerical solution obtained by applying operator splitting , Mathematical and Computer Modelling , 2007.

The five most important publications:

1. I. Faragó, J. Karátson. Numerical solution of nonlinear elliptic problems via preconditioning operators. Theory and applications. Nova Science Publisher, New York, 402 p. 2002.

2. . I. Faragó, R. Horváth, Discrete maximum principle and adequate discretizations of linear parabolic problems, SIAM Scientific Computing, 28 (2006) 2313-2336.

3. I. Faragó, B. Gnandt, Á. Havasi, Additive and iterative splitting methods and their numerical investigation, Computers and Mathematics with Applications, 55 (2008) 2266-2279.

4. I. Faragó, P. Thomsen, Z. Zlatev, On the additive splitting procedures and their computer realization, Applied Mathematical Modelling, 32 (2008) 1552-1569.

5. I. Faragó, Á. Havasi, Consistency analysis of operator splitting methods for C₀- semigroups, Semigroup Forum, 74 (2007) 125-139

Activity in the scientific community, international relations

International Journal of Comp. Science in Eng. (editorial board), Open Mathematical Journal (editorial board),

organizer of eight international conferences and workshops; guest editor of six journal special issues,

coauthors from Denmark, Finland, Germany, Spain, Bulgaria and Ukraina

visiting professor at universities in Germany, Spain, Denmark, Canada, USA, Finland

Name: László Fehér

Date of birth: 1963

Highest degree (discipline): PhD.

Present employer, position: Eötvös University, assistant professor

Major Hungarian scholarships: Bolyai scholarship (2007–2009)

Teaching activity (with list of courses taught so far):

Eötvös University (1987– 92, 2001-):

analysis (practice and lecture), Topology (practice and lecture)

Algebraic topology, Differential Geometry (practice and lecture)

Differential topology, Complex functions (practice), Equivariant cohomology, Spin Geometry.

Univ. Of Notre Dame USA (1993-97) Calculus all level (practice)

Introductory Math (lecture) 1998

Budapest Semester in Math. (2000-2002)

Topology Algebraic topology, (practice and lecture)

Other professional activity:

20 years of teaching experience, 4 diploma thesis supervisions, 1 Ph.D. thesis supervision;

over 20 lectures at international conferences;

14 publications;

Up to 5 selected publications from the past 5 years:

1. The degree of the discriminant of irreducible representations, elfogadva: Journal of Algebraic Geometry math.AG/0502500 (with Richárd Rimányi and András Némethi)

2. Schur and Schubert polynomials as Thom polynomials - Cohomology of moduli spaces (with Richárd Rimányi) Cent. European J. Math. 4 (2003) 418—434

3. On the structure of Thom polynomials of singularities, Bull. London Math. J. 39 (2007), 541-549 (with Richárd Rimányi)

4. Positivity of quiver coefficients (with A. S. Buch, Richárd Rimányi) Adv. Math. . 197 (2005) 306-320

5. On second order Thom-Boardman singularities: Fundamenta Mathematica 191 (2006), 249-264 (with Balázs Kőműves)

The five most important publications:

1. The degree of the discriminant of irreducible representations, elfogadva: Journal of Algebraic Geometry math.AG/0502500 (with Richárd Rimányi and András Némethi)

2. Schur and Schubert polynomials as Thom polynomials - Cohomology of moduli spaces (with Richárd Rimányi) Cent. European J. Math. 4 (2003) 418--434

3. On the structure of Thom polynomials of singularities, Bull. London Math. J. 39 (2007), 541-549 (with Richárd Rimányi)

4. Positivity of quiver coefficients (with A. S. Buch, Richárd Rimányi) Adv. Math. . 197 (2005) 306-320

5. On second order Thom-Boardman singularities: Fundamenta Mathematica 191 (2006), 249-264 (with Balázs Kőműves)

Activity in the scientific community, international relations

Name: Alice Fialowski

Date of birth: 1951

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi Professors’ Scholarship (1998–2001) , Széchenyi scholarship (2002– 2006)

Teaching activity (with list of courses taught so far):

Eötvös University (1974-79, 1994– ), BUTE (1984–94), Univ. of Pennsylvania, Philadelphia

(1987–1989), Univ. of California, Davis (1990–1995),

complex analysis, functiopnal analysis, calculus and probability theory, introductory calculus,

real analysis, algebra, intorductory analysis, Lie groups and Lie algebras, multivariate analysis, linear algebra, applied linear algebra, elements of analysis, infinite dimensional Lie algebras, cohomolgy of Lie algebras

Other professional activity:

Over 27years of teaching experience, 51 research papers, several diploma and Ph.D. students, a large number of ivited lectures in 18 countries

Up to 5 selected publications from the past 5 years:

Fialowski, A., Schlichenmaier, M., „Krichever-Novikov algebras as global deformations of the Virasoro algebra”, Comm. Contemp. Math. 5, No. 6 (2003), 921-945.

Fialowski, A., de Montigny, M., ,,On Deformations and Contractions of Lie Algebras”, J. Physics A: Math. Gen., 38 (2005), 649-663.

Fialowski, A., Penkava, M., „ Strongly homotopy Lie algebras of one even and two odd dimensions”, Math. QA/0308016, Jour. of Algebra vol. 283(2005), 125-148.

Fialowski, A., Millionschikov, D.: ,,Cohomology of graded Lie algebras of maximal class”, Journal of Algebra, 296 (2006), 157-176.

Fialowski, A., Wagemann, F., ,,Cohomology and deformations of the infinite diemsnional filiform Lie algebra m_0”, Journal of Algebra 318 (2007), 1002-1026.

The five most important publications:

Fialowski, A., „Deformations of Lie algebras”, Mat. Sbornyik USSR, 127 (169), (1985), 476-482; English translation: Math USSR-Sb., 55 (1986), no.2., 467-473.

Fialowski, A., „Ont he cohomology of infinite dimensional nilpotent Lie algebras”, Adv. In Math., 97 (1993), 267-277-

Fialowski, A., Fuchs, D.B., „Construction of Miniversal Deformations of Lie Algebras”, Jour. of Func. Anal. (1999), 161(1), 76-110.

Fialowski, A., Penkava, M., „Deformation Theory of Infinity Algebras”, Jour. of Algebra, 255 (2002), 59-88.

Fialowski, A., Schlichenmaier, M., „Global Deformations of the Witt Algebra of Krichever-Novikov Type”, Comm. in Contemporary Math., 5 (2003), 921-945.

Activity in the scientific community, international relations

Member of the Bolyai Mathematical Society, of the AMS, EMS

Member of the committee for international relations of the AMS (1993–1996)

Member of several conferences amd workshops (e.g. Lie algebras and Lie groups, 1995, Oberwolfach Conference 1996, 2006, 2010, Seminar Sophus Lie 2007)

Humboldt Fellowship (1986–1988)

NSF-OTKA grant with Michael Penkava (Univ. of Wisconsin.)

NATO grant Marc de Montigny, Univ. Albert, Canada.

Member of the editorial board for Journal of Lie theory, Journal of Generalized Lie theory and Appl., Springer book series Algebra and Applications

Name: András Frank

Date of birth: 1949

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, full professor

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1997–2000)

Teaching activity (with list of courses taught so far):

Eötvös University (22 years):

Operations research, graph theory, matroid theory, ployhedral combinatorics, combinatorial algorithms, Structures in combinatorial optimization

Other professional activity:

Guest researcher at University of Bonn (1984–1986, 1989–1993)

Over 70 publications, over 900 citations in about 500 publications

7 Ph.D. supervisions

invited addresses at the British Conference of Combinatorics (1993), at the Symposium on Mathematical Programming in Ann Arbour (1994), at the International Mathematical Congress (1998), over 60 other conference lectures

Grünwald Prize (1979), Science Award (Eötvös University, 1996), Bolyai Farkas Prize (2001), Szele Tibor Prize (2002)

Up to 5 selected publications from the past 5 years:

1. A. Frank, T. Király, and M. Kriesell, On decomposing a hypergraph into k-connected sub-hypergraphs, in: Submodularity, (guest editor S. Fujishige) Discrete Applied Mathematics, Vol. 131, Issue 2. (September 2003). pp. 373-383.

2. A. Frank, T. Király, and Z. Király, On the orientation of graphs and hypergraphs, in: Submodularity, (guest editor S. Fujishige) Discrete Applied Mathematics, Vol. 131, Issue 2. (September 2003). pp. 385-400.

3. A Frank, Restricted t-matchings in bipartite graphs, in: Submodularity, (guest editor S. Fujishige) Discrete Applied Mathematics, Vol. 131, Issue 2. (September 2003). pp. 337-346.

4. A. Frank and T. Király, Combined connectivity augmentation and orientation problems, in: Submodularity, (guest editor S. Fujishige) Discrete Applied Mathematics, Vol. 131, Issue 2. (September 2003). pp. 401-419.

The five most important publications:

1. A. Frank, An algorithm for submodular functions on graphs, Annals of Discrete Mathematics, 16 (1982) 97-120.

2. A. Frank, Edge-disjoint paths in planar graphs, J. of Combinatorial Theory, Ser. B. No. 2 (1985), 164-178.

3. A. Frank, Augmenting graphs to meet edge-connectivity requirements, SIAM J. on Discrete Mathematics, (1992 February), Vol.5, No 1., pp.22-53. A preliminary version

4. A. Frank and T. Jordán, Minimal edge-coverings of pairs of sets, J. Combinatorial Theory, Ser. B. Vol. 65, No. 1 (1995, September) pp. 73-110.

5. A. Frank and Z. Király, Graph orientations with edge-connection and parity constraints, Combinatorica, Vol. 22, No. 1. (2002), pp. 47-70.

Activity in the scientific community, international relations

member of organizing and program committees for seven international conferences

member ships: Bolyai Matematical Society, AMS, SIAM, Operations Research Committee of the Hungarian Academy of Sciences, Applied Mathematics Committee of the European Mathematical Society, granting committee of the Hungarian NSRF (OTKA) (1997–2000), Széchenyi Scholarship Committee (1998), several other award committees

member of the editorial board of SIAM Journal on Discrete Mathematics

leader of several OTKA projects (1995–1998, 1999–2001, 2002–2005), OTKA project for Hungarian–Dutch cooperation (2001–2004), AMFK (1995), DONET (Discrete Optimization Network, 1993-1998), Hungarian–Israeli cooperation project ADONET (2003– ), European cooperaton, France Telekom (2002–2005), Egervárz Research Group (2001– )

guest editor of one volume for Mathematical Programming, series B

Name: Róbert Freud

Date of birth: 1947

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, Mathematical Institute, Department of Algebra and Number Theory, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi professor's scholarship (1997–2000)

Teaching activity (with list of courses taught so far):

Eötvös University , Department of Algebra and Number Theory since1968

nearly all algebra and number theory courses for students in pure mathematics and teacher training.

Teaching also combinatorics and analysis at several universities in the USA as visiting faculty.

Other professional activity:

The performance in mathematics and its instruction and popularization are marked by the

following prizes:

National Contest for Secondary School Students (1964),

Who Is Good in Science (1964),

Schweitzer Memorial Competition (1967),

National Conference for Students in Scientific Research (1969, 1970),

Rényi Kató Prize (for scientific results as a university student, 1970),

Grünwald Géza Prize (for scientific results as a young researcher 1976),

Oustanding Instructor of Eötvös University Faculty of Science (1989, 2003),

Pro Universitate Medal (1996),

Beke Manó Prize (for popularization of mathematics 1997).

Up to 5 selected publications from the past 5 years:

1. Linear Algebra, university textbook, 518 pages, ELTE Eötvös Kiadó (1996-2007, six editions)

2. Number Theory, university textbook (with Edit Gyarmati), Nemzeti Tankönyvkiadó 2000, 740 pages, improved edition 2006, 810 pages.

The five most important publications:

1. Linear Algebra, university textbook, 518 pages, ELTE Eötvös Kiadó (1996-2007, six editions)

2. Number Theory, university textbook (with Edit Gyarmati), Nemzeti Tankönyvkiadó 2000, 740 pages, improved edition 2006, 810 pages.

3. On sets characterizing additive arithmetical functions I-II, Acta Arithmetica 35 (1979), 333-343, és 37 (1980), 35-41;

4. On disjoint sets of differences (with Paul Erdős), J. Number Theory 18 (1984), 99-109;

5. On sums of a Sidon-sequence (with Paul Erdős), J. Number Theory 38 (1991), 196-205.

Activity in the scientific community, international relations

organization of international conferences (ICME-6, colloquia in number theory),

committee member of Schweitzer Memorial Competition,

chair of committee of National Contest for Secondary School Students,

popularization of mathematics (lectures, papers, translation of books, postgradual training of teachers),

member of educational committees of Eötvös University Faculty of Science and of teacher training in mathematics.

Name: Katalin Fried

Date of birth: 1958

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate college professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1982– )

algebra, number theory, numerical methods, informatics, elementary mathematics, analysis tutorial

Other professional activity:

over 25 years of teaching experience

a large number of lectures in conferences on didactics

several books for elementary schools students

Up to 5 selected publications from the past 5 years:

n elem permutációi rekurzió nélkül, Tanárképzés–Tanártovábbképzés, 2002.

Matematikai csemegék, Matematikai Módszertani Lapok, Budapest, 3–4. (2002), 9–11.

További váratlan kérdések a bűvös négyzetről, Kőszegi matematikatanári konferencia-kötet, 2004

Matematika 5–8. tankönyv (társszerzőkkel), Nemzeti Tankönyvkiadó, 2004-2007.

The five most important publications:

Rare Bases For Finite Intervals of Integers, Acta Math. Sci. Szeged, Vol. 52 (1988), 303–305.

Rare Bases of Order h, Annales Univ. Sci. Budapest., 37 (1994) 243–245.

A note on a multiplicative problem, Annales Univ. Sci. Budapest., 40 (1997), 187–190.

A proof of Escher's (only?) theorem, Annales Univ. Sci. Budapest., 43. (2000), 159–163.

Activity in the scientific community, international relations

Member of the Bolyai Mathematical Society

Technical editor of the Annales Budapest. Sect. Mathematica

Name: Róbert Fullér

Date of birth: 1958

Highest degree (discipline): diploma in program-designer mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi Professor Scholarship (1998–2001), Széchenyi István Scholarship (2003-2006)

Teaching activity (with list of courses taught so far):

Eötvös Loránd University (1993– ):

Investments Analysis (for students in mathematics; lecture)

Decision Analysis (for students in mathematics; lecture, practice)

Operations Research Models (for students in mathematics; practice)

Multiple Objective Optimization (for students in mathematics; lecture)

Financial Mangement (for students in mathematics; lecture, practice)

Other professional activity:

15 years of teaching experience

Up to 5 selected publications from the past 5 years:

1. Christer Carlsson, Mario Fedrizzi and Robert Fullér, Fuzzy Logic in Management,

Kluwer Academic Publishers, Boston, 2003.

2. Christer Carlsson, Robert Fullér and Péter Majlender, On possibilistic correlation, Fuzzy Sets and Systems, 155(2005) 425-445.

3. Christer Carlsson, Robert Fullér, Markku Heikillä and Péter Majlender, A fuzzy approach to R&D project portfolio selection, International Journal of Approximate Reasoning, 44(2007) 93-105.

4. Robert Fullér and Péter Majlender, On interactive fuzzy numbers, Fuzzy Sets and Systems, 143(2004) 355-369.

5. Robert Fullér and Péter Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems, 136(2003) 363-374.

The five most important publications:

1. Robert Fullér, Introduction to Neuro-Fuzzy Systems, Springer, 2000.

2. Christer Carlsson and Robert Fullér, Fuzzy Reasoning in Decision Making and Optimization, Springer, 2002.

3. Robert Fullér and Péter Majlender, On obtaining minimal variablity OWA operator weights, Fuzzy Sets and Systems, 136(2003) 203-215.

4. Robert Fullér and Péter Majlender, An analytic approach for obtaining maximal entropy OWA operator weights, Fuzzy Sets and Systems, 124(2001) 53-57.

5. Christer Carlsson and Robert Fullér, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, 122(2001) 315-326.

Activity in the scientific community, international relations

Referee for:

Fuzzy Sets and Systems, Information Sciences, IEEE Transactions on Fuzzy Systems, Soft

Computing, European Journal of Operational Research, IEEE Transactions on Neural

Networks, Il Nuovo Cimento B, The Journal of the Franklin Institute, IEEE Transactions on

Systems, Man, and Cybernetics, Soochow Journal of Mathematics, Acta Mathematica

Hungarica, Omega - The International Journal of Management Science, Applied Artificial

Intelligence, Computers & Industrial Engineering, IEEE Transactions on Instrumentation and

Measurement, International Journal of Neural Systems, International Journal of Uncertainty,

Fuzziness and Knowledge-Based Systems, International Journal of Mathematics and

Mathematical Sciences, Acta Cybernetica, Journal of Modelling in Management, International

Journal of Approximate Reasoning, Computers and Mathematics with Applications, Fuzzy

Optimization and Decision Making, International Journal of Systems Science, Environmental

Modelling & Software, Knowledge and Information Systems, European Journal of Industrial

Engineering. Reviewer for Mathematical Reviews.

Name: Vince Grolmusz

Date of birth: 1961

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, full professor

Scientific degree (discipline): PhD, CSc, DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (2002–2005)

Teaching activity (with list of courses taught so far):

Eötvös University (1990– ): Combinatorics, computer science

BSM (1988–98 ) Introduction to Computing

Other professional activity:

18 years of teaching experience, 10 diploma thesis supervisions, 3 Ph.D. thesis supervisions;

over 30 lectures at international conferences; 26 publications in journals; 8 US patents;

Up to 5 selected publications from the past 5 years:

Grolmusz, V.: Computing Elementary Symmetric Polynomials with a Sub-Polynomial Number of Multiplications, SIAM Journal on Computing, Vol. 32, No. 6 (2003), pp 1475-1487.

Grolmusz, V.: A Note on Set Systems with no Union of Cardinality 0 Modulo m, Discrete Mathematics and Theoretical Computer Science (DMTCS) Vol 6, No. 1 (2003), pp 41-44.

Grolmusz, V., Tardos, G.: A Note on Non-Deterministic Communication Complexity with Few Witnesses, Theory of Computing Systems, Vol 36, No. 4 (2003), pp 387-391.

Grolmusz, V.: A Note on Explicit Ramsey Graphs and Modular Sieves, Combinatorics, Probability and Computing Vol. 12, (2003) pp. 565-569 (an invited paper).

Grolmusz, V.: Constructing Set-Systems with Prescribed Intersection Sizes, Journal of Algorithms, Vol. 44 (2002), pp. 321-337.

The five most important publications:

Grolmusz, V.: Computing Elementary Symmetric Polynomials with a Sub-Polynomial Number of Multiplications, SIAM Journal on Computing, Vol. 32, No. 6 (2003), pp 1475-1487.

Grolmusz, V.: Constructing Set-Systems with Prescribed Intersection Sizes, Journal of Algorithms, Vol. 44 (2002), pp. 321-337.

Grolmusz, V., Sudakov, B.: k-wise Set-Intersections and k-wise Hamming-Distances, J. Combin. Theory Ser. A 99 (2002), no. 1, 180--190.

Grolmusz, V.: Separating the Communication Complexities of MOD m and MOD p Circuits, Journal of Computer and Systems Sciences, Vol. 51, (1995), No. 2

Grolmusz, V., Tardos, G.: Lower Bounds for (MOD p, MOD m) Circuits, SIAM Journal on Computing, Vol. 29, (2000), No. 4, pp. 1209-1222

Grolmusz, V.: Superpolynomial Size Set-Systems with Restricted Intersections mod 6 and Explicit Ramsey Graphs, Combinatorica, Vol. 20, (2000), No. 1, pp. 73-88.

Activity in the scientific community, international relations

Visiting prof at the University of Chicago, 1999; Coordinator of EU FP5, FP6 and large Hungarian research projects.

Name: Katalin Gyarmati

Date of birth:

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Teaching activity (with list of courses taught so far):

Eötvös University (1999– ):

number theory (for students in mathematics; practice)

linear algebra (for students in informatics; practice)

computational number theory (for students in mathematics, lecture)

exponential sums and its applications in number theory (for students in mathematics, lecture)

Other professional activity:

9 years of teaching experience, over 16 lectures at international conferences;

24 publications.

Up to 5 selected publications from the past 5 years:

1. K. Gyarmati, A. Sárközy, Equations in finite fields with restricted solution sets, I. (Character sums.) , Acta Math. Hungar. 118 (2008), 129-148.

2. K. Gyarmati, A. Sárközy, Equations in finite fields with restricted solution sets, II. (Algebraic equations.), Acta Math. Hungar. 119 (2008), 259-280.

3. K. Gyarmati, S. Konyagin, I. Z. Ruzsa, Double and triple sums modulo a prime, CRM Proceedings & lecture Notes, Volume 43, AMS 2008, 271-278.

4. K. Gyarmati, On the number of divisors which are values of a polynomial, The Ramanujan Journal, to appear.

5. K. Gyarmati, M. Matolcsi, I. Z. Ruzsa, A superadditivity and submultiplicativity properties for cardinalities of sumsets, Combinatorica, to appear.

The five most important publications:

1. K. Gyarmati, On a problem of Diophantus, Acta Arith. 97.1 (2001), 53-65.

2. K. Gyarmati, On the correlation of binary sequences, Studia Sci. Math. Hungar. 42 (2005), 59-75.

3. K. Gyarmati, A. Sárközy, A. Pethõ, On linear recursion and pseudorandomness, Acta Arith. 118 (2005), 359-374.

4. K. Gyarmati, A. Sárközy, Equations in finite fields with restricted solution sets, I. (Character sums.) , Acta Math. Hungar. 118 (2008), 129-148.

5. K. Gyarmati, M. Matolcsi, I. Z. Ruzsa, A superadditivity and submultiplicativity properties for cardinalities of sumsets, Combinatorica, to appear

Activity in the scientific community, international relations

Középiskolai Matematikai Lapok (editor in chief, 1996–1999)

member of OTKA (2003-)

coauthors from France, Canada, Germany and Hungary.

Name: Gábor Halász

Date of birth: 1941

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, Department of Analysis, professor

Scientific degree (discipline): fellow of HAS (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

For over 20 years:

Introduction to Complex Functions, Fourier Integral, Geometric Function Theory, Riemann Surfaces, Chapters from Complex Function Theory, Special Functions, Approximation Theory.

Special courses: Analysis in Probability, Tauberian Theorems, Arithmetic Functions.

Other professional activity:

1964-1991: Alfréd Rényi Institute of Mathematics of HAS (1976-1991: head of the Function Theory Department)

Up to 5 selected publications from the past 5 years:

The five most important publications:

Über die Mittelwerte multiplikativer zahlentheretischer Funktionen, Acta Math. Hung. 19(1968), 365-403.

On the distribution of roots of Riemann zeta and allied functions I, J. Number Theory 1(1969), 121-137 (Turán Pállal közösen).

Tauberian theorems for univalent functions, Studia Sci. Math. Hung. 4(1969), 421-440.

Estimates for the concentration function of combinatorial number theory and probability, Per. Math. Hung. 8(1977), 197-211.

On Roth's method in the theory of irregularities of point distributions, Recent Progress in Analytic Number Theory, vol. 2, Academic Press (1981), 79-94.

Activity in the scientific community, international relations

János Bolyai Mathematical Society (committee member), Doctoral Committee of Section Mathematics of HAS (member), member of the editorial boards of Acta Math. Hung., Studia Sci. Math. Hung., Analysis, Acta Arithmetica.

Name: Norbert Hegyvári

Date of birth: 1956

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, professor of college

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Eötvös University (1985– ):

algebra (for students in mathematics; lecture, practice)

analysis (for students mathematics; lecture, practice)

probability theory (for students mathematics; lecture, practice) at ELTE Teacher Training College,

analysis (for students mathematics; lecture, practice), at Dept. of Analysis

Other professional activity:

20 years of teaching experience, ~30 diploma thesis supervisions,;

~15 lectures at international conferences;

39 publications;

2 books;

Up to 5 selected publications from the past 5 years:

[1] Hegyvári, N, F. Hennecart and A. Plagne, A proof of two Erdős' conjectures on restricted addition and further results ( Journal fuer die reine und angewandte Mathematik (Crelle) 560 2003, 199–220 )

[2] On Combinatorial Cubes, The Ramanujan Journal 8 (2004), no.3, 303-307

[3] Arithmetical and group topologies, Acta Math. Hungar. 106 (3) (2005), 187-195

[4] On intersecting properties of partitions of integers Combin. Probab. Comput. (14) 03, (2005), 319-323

[5] Answer to the Burr-Erdős question on restricted addition
and further results, Combinatorics, Probability and Computing,
Volume 16, Issue 05, Sep 2007, pp 747-756
(with F. Hennecart and A. Plagne)

The five most important publications:

[1] Hegyvári, N, F. Hennecart and A. Plagne, A proof of two Erdős' conjectures on restricted addition and further results (Journal fuer die reine und angewandte Mathematik (Crelle) 560, 2003, 199–220)

[2] Hegyvári, N, F. Hennecart, On Monochromatic sums of squares and primes, Journal of Number Theory, Volume 124, Issue 2,
June 2007, Pages 314-324

[3] Hegyvári, Norbert, On the representation of integers as sums of distinct terms from a fixed set Acta Arith. 92.2 2000. 99–104.

[4] Hegyvári, On the dimension of the Hilbert cubes. J. Number Theory 77
(1999), no. 2, 326--330.

[5] N.Hegyvári, A Sárközy, On Hilbert cubes in certain sets. Ramanujan J. 3 (1999), no.3, 303--314.

Activity in the scientific community, international relations

organizer of two international conferences;;

coauthors from England, France, China

visiting (for a month) at universities in Germany, England, France, USA;

Name: Peter Hermann

Date of birth: 1953

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Teaching activity (with list of courses taught so far):

Eötvös University (1977– ):

algebra and number theory (for students in mathematics; lecture, practice)

BSM (1993– )

Basic and advanced algebra (lecture, practice)

CEU (2004– )

Basic Algebra I (for Ph.D. students in mathematics)

Other professional activity:

30 years of teaching experience, more than 10 diploma thesis supervisions, 1 Ph.D. (CSc) thesis supervision;

lectures at international conferences;

15 publications

Up to 5 selected publications from the past 5 years:

The five most important publications:

1. On the product of all elements in a finite group (with J. Dénes), Annals of Discrete Math. 15 (1982), 107-111. (MR 86c:20024; 20D60(05B15))

2. Separability properties of finite groups hereditary for certain products (with K. Corrádi and L. Héthelyi), Arch. Math. 44 (1985), 210-215. (MR 86d:20025; 20D40 (20D20))

3. On the product of all nonzero elements of a finite ring, Glasgow Math. J. 30 (1988), 325-330. (MR 89m:16027; 16A44)

4. On p-quasinormal subgroups in finite groups, Arch. Math. 53 (1989), 228-234.(MR 90i:20028; 20D40(20D20))

5. On finite p-groups with isomorphic maximal subgroups, J. Austral. Math. Soc. (Series A) 48 (1990), 199-213. (MR 91a:20024; 20D15)

Activity in the scientific community, international relations

KöMaL (Mathematical and Physical Journal for Secondary Schools; member of the Editorial Board in Mathematics), 1988–;

Name: Tibor Illés

Date of birth: 1963

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Loránd University, associate professor

Scientific degree (discipline): phd (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1992– ):

operations research (for students in (applied) mathematics; lecture, practice)

linear programming (for students in (applied)mathematics; lecture)

nonlinear programming (for students in (applied) mathematics; lecture)

game theory (for students in (applied) mathematics; lecture)

continuous optimization (for students in (applied) mathematics; lecture)

discrete programming (for students in (applied) mathematics; lecture)

Other professional activity:

Research projects: 11 projects in applied mathematics ( 4 times as participant, 7 times as

project head), 5 OTKA projects in basic research (3 times as participant, 2 times as project head)

Publications: 33 journal articles, 9 chapters in edited volumes, 24 working papers, 21 research reports,

Up to 5 selected publications from the past 5 years:

1. Akkeles, A. A., Balogh L. and Illés T., New variants of the criss-cross method for linearly constrained, convex quadratic programming, European Journal of Operational Research, Vol. 157, No. 1:74-86, 2004.

2. Illés T. and Terlaky T., Pivot Versus Interior Point Methods: Pros and Cons, European Journal of Operational Research, 140:6-26, 2002.

3. Boratas-Sensoy, Z., Illés T. and Kas P., Entropy and Young Programs: Relations and Self-concordance, Central European Journal of Operations Research, 10:261-276, 2002.

4. Illés T., Peng, J., Roos, C. and Terlaky T., A Strongly Polynomial Rounding Procedure Yielding A Maximally Complementary Solution for P*(κ) Linear Complementarity Problems, SIAM Journal on Optimization, 11:320-340, 2000.

5. Illés T. and Pisinger, D., Upper Bounds on the Covering Number of Galois-planes with Small Order, Journal on Heuristics, 7:59-76, 2000.

The five most important publications:

1. Illés T., Peng, J., Roos, C. and Terlaky T., A Strongly Polynomial Rounding Procedure Yielding A Maximally Complementary Solution for P*(κ) Linear Complementarity Problems, SIAM Journal on Optimization, 11:320-340, 2000.

2. Illés T. and Kassay G., Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming, Journal of Optimization Theory and Applications, 101:243-257, 1999.

3. Illés T. and Kassay G., Farkas Type Theorems for Generalized Convexities, Pure Mathematics and Applications 5:225-229, 1994.

4. Illés T., Mayer J. and Terlaky T., Pseudoconvex Optimization for a Special Problem of Paint Industry, European Journal of Operations Research 79:537-548, 1994.

5. Illés T., Szőnyi T. and Wettl F., Blocking Sets and Maximal Strong Representative Systems in Finite Projective Planes, Proceedings of the Conference "Blocking Sets", Giessen, 97-107, 1991.

Activity in the scientific community, international relations

Member of János Bolyai Mathematical Society, Hungarian Operations Research Society,

Mathematical Programming Society, EUROPT WG, EURO Working Group on Continuous

Optimization

Name: Ferenc Izsák

Date of birth: 1976

Highest degree (discipline): diploma in pure mathematics

Present employer, position: Eötvös University, teaching assistant

Scientific degree (discipline): PhD (applied mathematics)

Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):

Eötvös University (2001– ):

analysis (for students in applied mathematics, physics; practice)

introductory mathematics (for students in biology, environmental study, chemistry; lecture, practice)

partial differential equations (for students in applied and pure mathematics, meteorology; practice)

finite element methods (for students in the mathematics doctoral school; lecture)

mathematical modeling (for students in applied mathematics; lecture)

Other professional activity:

7 years of teaching experience,

21 publications;

Up to 5 selected publications from the past 5 years:

1. Izsák, F., Lagzi, I.: Simulation of Liesegang pattern formation using a discrete stochastic model, Chemical Physics Letters, 371(3-4) (2003), 321-326.

2. Izsák, F.: An existence theorem for a type of functional differential equations with infinite delay, Acta Math. Hung., 108(1-2) (2005), 135-151.

3 van der Vegt, J.J.W., Izsák, F., Bokhove, O.: Error analysis of a continuous- discontinuous Galerkin finite element method for generalized 2D vorticity dynamics, SIAM Journal on Numerical Analysis, 45(4) (2007), 1349-1369.

4. Izsák, F., Harutyunyan, D., van der Vegt, J.J.W.: Implicit a posteriori error estimates for the Maxwell equations, Mathematics of Computation, 77(263) (2008), 1355=1386.

5. Harutyunyan, D., Izsák, F., van der Vegt, J.J.W.: Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates, Computer Methods in Applied Mathematics and Engineering, 197(17-18) (2008), 1620-1638.

The five most important publications

1. Izsák, F., Lagzi, I.: Simulation of Liesegang pattern formation using a discrete stochastic model, Chemical Physics Letters, 371(3-4) (2003), 321-326.

2. Izsák, F.: An existence theorem for a type of functional differential equations with infinite delay, Acta Math. Hung., 108(1-2) (2005), 135-151.

3. van der Vegt, J.J.W., Izsák, F., Bokhove, O.: Error analysis of a continuous- discontinuous Galerkin finite element method for generalized 2D vorticity dynamics, SIAM Journal on Numerical Analysis, 45(4) (2007), 1349-1369.

4. Izsák, F., Harutyunyan, D., van der Vegt, J.J.W.: Implicit a posteriori error estimates for the Maxwell equations, Mathematics of Computation, 77(263) (2008), 1355-1386.

Activity in the scientific community, international relations

coordinator with the Erasmus – programme (University of Twente)

active research collaboration with the University of Twente;

coauthors from the Netherlands, Russian Federation, Armenia;

Name: Tibor Jordán

Date of birth: 1967

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Eötvös University (1991–1994, 2000– ):

computer science, discrete mathematics, graph theory, theory of computing, scheduling theory, combinatorial algorithms, combinatorial structures, approximation algorithms

Technical University of Budapest (1994–1996):

algebra, analysis, discrete mathematics

University of Odense (1996–1998):

connectedness of graphs

University of Aarhus (1999)

combinatorial optimization, discrete mathematics

Other professional activity:

over 50 reasearch articles, over 200 citations, over 50 conference lectures

coauthor of one book

project leader of one OTKA and one FKFP project

Rényi Kató Prize (1991), ), Grünwald Géza Prize (1996).

managing editor of Combinatorica

long term visits at several universities (Bonn, Amsterdam, Odense, Grenoble, Kyoto, Aarhus)

Up to 5 selected publications from the past 5 years:

A. Berg, T. Jordán, A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid, J. Combinatorial Theory, Ser. B., Vol. 88, 77-97, 2003.

B. Jackson, T. Jordán, Non-separable detachments of graphs, J. Combinatorial Theory, Ser. B., Vol. 87, 17-37, 2003.

T. Jordán, Z. Szigeti, Detachments preserving local edge-connectivity of graphs, SIAM J. Discrete Mathematics, Vol. 17, No. 1, 72-87 (2003).

B. Jackson, T. Jordán, Connected rigidity matroids and unique realizations of graphs, J. Combinatorial Theory, Ser. B., in press

B. Jackson, T. Jordán, Independence free graphs and vertex-connectivity augmentation, J. Combinatorial Theory, Ser. B., in press

The five most important publications, besides the ones given above:

T. Jordán, On the optimal vertex-connectivity augmentation, J. Combinatorial Theory, Ser. B., Vol. 63, 8-20, 1995.

A. Frank, T. Jordán, Minimal edge-coverings of pairs of sets, J. Combinatorial Theory, Ser. B., Vol. 65, 73-110, 1995.

J. Bang-Jensen, H.N. Gabow, T. Jordán and Z. Szigeti, Edge-connectivity augmentation with partition constraints, SIAM J. Discrete Mathematics Vol. 12, No. 2, 160-207 (1999).

Activity in the scientific community, international relations

Member of the Bolyai János Mathematical Society

Long term visitor at University of Aarhus (Denmark), Odense University (Denmark), Queen Mary College, London (Great Britain), Hiroshima University (Japan).

Name: Alpár Jüttner

Date of birth: 1975

Highest degree (discipline): MSc in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1998– ):

operations research (for students in mathematics and in informatics; practice)

complexity theory (for students in matematics; practice)

Other professional activity:

5 years of teaching experience, 3 MSc thesis supervisions,

over 10 international conference appearances;

24 publications;

2 international patents;

Up to 5 selected publications from the past 5 years:

[1] Csaba Antal, János Harmatos, Alpár Jüttner, Gábor Tóth, and Lars Westberg. Cluster-based resource provisioning method for optical backbone. Journal of Optical Networking, 5(11):829-840, October 2006.

[2] Alpár Jüttner. On budgeted optimization problems. SIAM Journal on Discrete Matemathics, 20(4):880-892, 2006.

[3] Alpár Jüttner. Optimization with additional variables and constraints. Operations Research Letters, 33(3):305-311, May 2005.

[4] Alpár Jüttner and Ádám Magi. Tree based broadcast in ad hoc networks. Mobile Networks and Applications (MONET) - Special Issue on “WLAN Optimization at the MAC and Network Levels”, 10(5):753-762, oct 2005.

[5] Alpár Jüttner, András Orbán, and Zoltán Fiala. Two new algorithms for UMTS access network topology design. European Journal of Operational Research, 164(2):456-474, July 2005.

The five most important publications:

[1] Alpár Jüttner. On budgeted optimization problems. SIAM Journal on Discrete Matemathics, 20(4):880-892, 2006.

[2] Alpár Jüttner. Optimization with additional variables and constraints. Operations Research Letters, 33(3):305-311, May 2005.

[3] Alpár Jüttner, András Orbán, and Zoltán Fiala. Two new algorithms for UMTS access network topology design. European Journal of Operational Research, 164(2):456-474, July 2005.

[4] Alpár Jüttner, István Szabó, and Áron Szentesi. On bandwidth efficiency of the hose resource management model in virtual private networks. In Infocom. IEEE, April 2003.

[5] Alpár Jüttner, Balázs Szviatovszki, Ildikó Mécs, and Zsolt Rajkó. Lagrange relaxation based method for the QoS routing problem. In Infocom. IEEE, April 2001.

Activity in the scientific community, international relations

2005-2008: COST293 Management Comittee member

2007-2009: Maire Curie Research Fellowship at University of Bedfordshire, Luton, UK

Name: János Karátson

Date of birth: 1966

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Magyary scholarship (1999-2002), Bolyai scholarship (2002–2005 and 2007-2010)

Teaching activity (with list of courses taught so far): at Eötvös University (since 1990):

functional analysis (for students in applied mathematics, basic level and specialization

in numerics; lecture, practice),

partial differential equations (for students in meteorology; lecture, practice),

ordinary differential equations (for students in physics; lecture, practice),

analysis, ordinary differential equations (for students in applied mathematics; practice)

MSc and PhD thesis supervisions: for students in (applied) mathematics

In English: translation of scientific texts (for Hungarian students), Mathematics (for foreign students)

Other professional activity:

52 papers and 1 monograph;

regular lectures in international conferences;

international collaborations (Netherlands, Bulgaria, USA, Sweden, Finland);

Up to 5 selected publications from the past 5 years:

[1] Axelsson, O., Karátson J., On the superlinear convergence of the conjugate gradient method for nonsymmetric normal operators, Numer. Math. 99 (2004), 197-223.

[2] Karátson J., Lóczi L., Sobolev gradient preconditioning for the electrostatic potential equation, Comput. Math. Appl. 50 (2005), pp. 1093-1104.

[3] Karátson J., Korotov, S., Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions, Numer. Math 99 (2005), No. 4, 669-698.

[4] J. Karátson, J. W. Neuberger, Newton's method in the context of gradients, Electron. J. Diff. Eqns. Vol. 2007(2007), No. 124, pp. 1-13.

[5] Axelsson, O., Karátson J., Mesh independent superlinear PCG rates via compact-equivalent operators, SIAM J. Numer. Anal., 45 (2007), No.4, pp. 1495-1516.

The five most important publications:

[1] Faragó I., Karátson J., Numerical solution of nonlinear elliptic problems via preconditioning operators: theory and application. Advances in Computation, Volume 11, NOVA Science Publishers, New York, 2002.

[2] Karátson J., Faragó I., Variable preconditioning via quasi-Newton methods for nonlinear problems in Hilbert space, SIAM J. Numer. Anal. 41 (2003), No. 4, 1242-1262.

[3]-[5]: same as above

Activity in the scientific community, international relations:

Collaboration with Prof. O. Axelsson (Nijmegen - Uppsala), I. Lirkov (Sofia), S. Korotov (Helsinki), J. Neuberger (North Texas).

Regular refereeing for international papers.

Membership in editorial board of Numer. Lin. Algebra.

Organization in two international conferences.

Visiting professorship in Helsinki.

Reviewing for AMS Mathematical Reviews and Zentralblatt.

Name: Gyula Károlyi

Date of birth: 1964

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi professor's scholarship (2000–2003)

Bolyai Fellowship (2003–2006, 2007–2010)

Teaching activity (with list of courses taught so far):

Eötvös University (1985– ):

algebra, number theory (for students in mathematics; lecture, practice)

linear algebra (for students in informatics; practice)

algebraic numbre theory, combinatorial geometry and number theory (for students in mathemtics and problem soling seminar)

ETH Zürich (2001–2002)

graph theory (for students in mathematics, informatics, engineering; lecture and practice)

University of Memphis

business calculus (for general audience; lecture)

combinatorial number theory (for students in mathematics; lecture)

Other professional activity:

23 years of teaching experience, 4 diploma thesis supervisions

coordinator and suervisor of undergraduate research at Eötvös University (1996–2006)

over 80 letctures at international conferences and seminars in renowned institutions around the world

35 publications in refereed international journals and volumes

Up to 5 selected publications from the past 5 years:

1. Károlyi, Gy., The Erdős–Heilbronn problem in abelian groups, Israle Journal of Mathematics 139 (2004), 349–359.

2. Károlyi, Gy., A compatness argument in the additive theory and the polynomial method, DiscreteMathematics 302 (2005), 124–144.

3. Károlyi, Gy., An inverse theorem for the restricted set addition in abelian groups, Journal of Algebra 290 (2005), 557–593.

4. Károlyi, Gy., Cauchy–Davenport theorem in group extensions, L’Enseignement Mathématique 51 (2005), 239–254.

5. Károlyi, Gy., A note on the Hopf–Stiefel function, European Journal of Combinatorics 27 (2006), 1135–1137.

The five most important publications:

1. Károlyi, Gy., Geometric discrepancy theorems in higher dimensions, Studia Scientiarum Mathematicrum Hungarica 30 (1995), 59–94.

2. Károlyi, Gy., Irregularities of point distributions relative to homothetic convex bodies I., Monatshefte für Mathematik 120 (1995), 247–279.

3. Dasgipta, S., Károlyi, Gy., Serra, O., Szegedy, B.: Transersals of additive latin squares, Israel Journal of Mathematics 126 (2001), 17–28.

4. Károlyi, Gy., An inverse th theorem for the restricted set addition in abelian groups, Journal of Algebra 290 (2005), 557–593.

5. Károlyi, Gy., Cauchy–Davenport theorem in group extensions, L’Enseignement Mathématique 51 (2005), 239–254.

Activity in the scientific community, international relations

Athematical and Physical Journal for Secondary Schools (editor), 1988– ;

organizer of an international conference, a workshop and a national undergraduate research conference;

member of the János Bolyai Mathematical Society and the Hungarian Humboldt Assocation;

chair of the Hungarian Mathematical Contest (1998–2002);

member of the granting committee of the Hungarian NSRF (OTKA), 2008–2010;

coauthors from Canada, the Czech Republic, Germany, Spain, Japan, Switzerland and the US;

visiting professor at universities in Switzerland and in the US;

visiting reserach fellow in France, in the Netherlands and in the US;

Name: Tamás Keleti

Date of birth: 1970

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Széchenyi Professor Scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Eötvös University (1992– ):

analysis (for students in mathematics; lecture, practice)

real functions (for students fourth and fifth year students in mathematics; lecture)

problem solving seminar in real analysis (for students in mathematics)

special courses (for students in mathematics): intuitive topology, discrete dynamical systems, mathematics of fractals

BSM (1999– )

Real functions and measures (lecture, practice)

Other professional activity:

16 years of teaching experience, 6 diploma thesis supervisions, 1 Ph.D. thesis supervisions;

lectures at international conferences;

26 publications;

Up to 5 selected publications from the past 5 years:

1. Udayan B. Darji and TK: Covering the real line with translates of a compact set, Proc. Amer. Math. Soc. 131 (2003), 2593-2596.

2. Márton Elekes and TK: Borel sets which are null or non-sigma-finite for every translation invariant measure, Adv. Math. 201 (2006), 102-115.

3. Gyula Károlyi, TK, Géza Kós and Imre Ruzsa: Periodic decomposition of integer valued functions, Acta Math. Hungar., to appear.

4. TK: Periodic decomposition of measurable integer valued functions, J. Math. Anal. Appl. 337 (2008), 1394-1403.

5. Bálint Farkas, Viktor Harangi, TK and Szilárd György Révész: Invariant decomposition of functions with respect to commuting invertible transformations , Proc. Amer. Math Soc. 136 (2008), 1325-1336.

The five most important publications:

1. TK: Difference functions of periodic measurable functions, Fund. Math. 157 (1998), no. 1, 15--32.

2. TK and David Preiss: The balls do not generate all Borel sets using complements and countable disjoint unions, Math. Proc. Cambridge Philos. Soc. 128 (2000), no. 3, 539-547.

3. Udayan B. Darji and TK: Covering the real line with translates of a compact set, Proc. Amer. Math. Soc. 131 (2003), 2593-2596.

4. Márton Elekes and TK: Borel sets which are null or non-sigma-finite for every translation invariant measure, Adv. Math. 201 (2006), 102-115.

Activity in the scientific community, international relations

organizer and often leader the team of the Eötvös University at the International Mathematics Competition, 1998- ;

coauthors from England, USA, Czech Republic and Greece;

Royal Society/NATO Postdoc scholarship at the University College London, 1997/98;

visiting research instructor at the Michigan State University, 1998/99

Name: Tamás Király

Date of birth: 1975.03.19

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Loránd University, assistant professor

Scientific degree (discipline): phd (mathematics)

Major Hungarian scholarships: Öveges scholarship, OM Postdoctoral fellowship

Teaching activity (with list of courses taught so far):

Eötvös University (1999– ):

Integer Programming I-II (for students in (applied)mathematics; lecture)

Matroid Theory (for students in (applied)mathematics; lecture)

Applied Module (Combinatorial Optimization) (for students in applied mathematics; practice)

Operations Research (for students in applied mathematics and informatics; practice)

Other professional activity:

Research fellow in the MTA-ELTE Egerváry Research Group on Combinatorial Optimization

Research projects: Öveges project “Structural properties of Networks”; joint research with France Telecom; participation in several OTKA projects

Publications: 9 journal articles, 10 research reports

Up to 5 selected publications from the past 5 years:

1. A. Frank, T. Király, M. Kriesell, On decomposing a hypergraph into k connected sub-hypergraphs, Discrete Applied Mathematics 131 (2003), 373-383.

2. A. Frank, T. Király, Z. Király, On the orientation of graphs and hypergraphs, Discrete Applied Mathematics 131 (2003), 385-400.

3. A. Frank, T. Király, Combined connectivity augmentation and orientation problems, Discrete Applied Mathematics 131 (2003), 401-419.

4. T. Király, Covering symmetric supermodular functions by uniform hypergraphs, Journal of Combinatorial Theory Series B 91 (2004), 185-200.

5. T. Király, J. Pap, Total dual integrality of Rothblum's description of the stable marriage polyhedron, Mathematics of Operations Research 33(2) (2008), 283-290.

The five most important publications:

1. A. Frank, T. Király, M. Kriesell, On decomposing a hypergraph into k connected sub-hypergraphs, Discrete Applied Mathematics 131 (2003), 373-383.

2. A. Frank, T. Király, Z. Király, On the orientation of graphs and hypergraphs, Discrete Applied Mathematics 131 (2003), 385-400.

3. A. Frank, T. Király, Combined connectivity augmentation and orientation problems, Discrete Applied Mathematics 131 (2003), 401-419.

4. T. Király, Covering symmetric supermodular functions by uniform hypergraphs, Journal of Combinatorial Theory Series B 91 (2004), 185-200.

5. T. Király, J. Pap, Total dual integrality of Rothblum's description of the stable marriage polyhedron, Mathematics of Operations Research 33(2) (2008), 283-290.

Activity in the scientific community, international relations

Participation in ADONET Marie Curie Research Training Network

Name: Zoltán Király

Date of birth: 1963

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Bolyai scholarship (1999–2002)

Teaching activity (with list of courses taught so far):

Eötvös University (1987– ):

Discrete mathematics (for students in mathematics and in informatics; lecture, practice)

Parallel algorithms (for students in mathematics and in informatics; lecture)

Data structures (for students in mathematics and in informatics; lecture)

Algorithms (for students in mathematics and in informatics; lecture)

Complexity theory (for students in mathematics and in informatics; lecture)

Graph theory (for students in mathematics; lecture, practice)

Combinatorial optimization (for students in informatics; lecture)

Introduction to computer science (for students in informatics; lecture, practice)

Interactive proofs (for students in mathematics; lecture)

Complexity seminar (for students in mathematics and in informatics; seminar)

Applied discrete mathematics seminar (for students in mathematics and in informatics; seminar)

CEU PhD school (2007 ):

Complexity theory (lecture)

Other professional activity:

21 years of teaching experience, 9 diploma thesis supervisions, 2 Ph.D. thesis supervisions;

over 20 lectures at international conferences;

16 publications in refereed journals;

1 international patent.

Up to 5 selected publications from the past 5 years:

A. Frank, T. Király, Z. Király: ,,On the orientation of graphs and hypergraphs'', Discrete Applied Mathematics 131 (2003), pp. 385-400.

M. Kano, G. Y. Katona, Z. Király: ,,Packing paths of length at least two'', Discrete Mathematics, 283, (2004), pp. 129-135.

V. Grolmusz, Z. Király: ,,Generalized Secure Routerless

Routing'', Lecture Notes in Computer Science 3421,

Networking - ICN 2005, part II, eds: P. Lorenz, P. Dini, (2005), pp. 454-462.

Z. Király, Z. Szigeti: ,,Simultaneous well-balanced orientations

of graphs'', JCT B 96, Issue 5, (2006), pp. 684-692.

A. Frank, Z. Király, B. Kotnyek: ,,An Algorithm for Node-Capacitated Ring Routing'',

Operations Research Letters, 35, Issue 3, (2007), pp. 385-391.

The five most important publications:

A. Gyárfás, Z. Király, J. Lehel: ,,On-line 3-chromatic graphs. I. Triangle--free graphs'',

SIAM J. Discr. Math. 12, (1999), pp. 385-411.

A. Frank, Z. Király: ,,Graph Orientations with Edge-connection and Parity Contstraints'', Combinatorica 22, (2002), pp. 47-70.

A. Frank, T. Király, Z. Király: ,,On the orientation of graphs and hypergraphs'', Discrete Applied Mathematics 131 (2003), pp. 385-400.

M. Kano, G. Y. Katona, Z. Király: ,,Packing paths of length at least two'', Discrete Mathematics, 283, (2004), pp. 129-135.

Z. Király, Z. Szigeti: ,,Simultaneous well-balanced orientations

of graphs'', JCT B 96, Issue 5, (2006), pp. 684-692.

Activity in the scientific community, international relations

Member of BJMT, ICA, EATCS;

visiting researcher at Rutgers, Princeton, Yale.

Name: Emil Kiss

Date of birth: 1956

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, full professor, Head of the Department of Algebra and Number Theory

Scientific degree (discipline): DSc (mathematics), dr habil

Major Hungarian scholarships: Széchenyi scholarship (1998–2001)

Teaching activity (with list of courses taught so far):

Eötvös University (from 1978, full time since 1989):

Classical, linear, abstract, universal algebra and number theory at various levels (for students in mathematics and in teacher training; lecture, practice).

La Trobe University, Australia (1986, three semesters):

algebra, complex analysis, foundations of mathematics (for students in mathematics and applied mathematics).

University of Illinois at Chicago (1990, two semesters):

linear algebra, differential equations, universal algebra (for students in mathematics and applied mathematics).

BSM

two courses (abstract algebra; group theory)

Other professional activity:

30 years of teaching experience, 2 diploma thesis supervisions;

over 10 invited plenary lectures at international conferences;

main advisor and organizer of the Students Scientific Association (1991-1997).

Committee member for the National High School Mathematical Competition.

Chairman of the BSc Committee of Education at ELTE.

39 publications with over 200 citations;

Up to 5 selected publications from the past 5 years:

1) K. A. Kearnes and E. W. Kiss, Residual smallness and weak centrality, Journal of Algebra and Computation, 13(2003), 35-59.

2) K. A. Kearnes and E. W. Kiss, The triangular principle is equivalent to the triangular scheme, Algebra Universalis, 54(2005), 373-383.

3) E. W. Kiss, M. A. Valeriote, On tractability and congruence distributivity. Logical Methods in Computer Science, 3(2:6, 2007), 20 pages.

4) Emil Kiss, Introduction to algebra, TypoTeX, 2007 (textbook, in Hungarian), 1000 pages.

The five most important publications:

1) A. Day and E.W. Kiss, Frames and rings in congruence modular varieties, Journal of Algebra, 109 (1987), no. 2, 479-507.

2) E. W. Kiss, M. A. Valeriote, Abelian algebras and the Hamiltonian property, Journal of Pure and Applied Algebra 87:1 (1993), 37-49.

3) K. A. Kearnes, E. W. Kiss, M. A. Valeriote, Minimal sets and varieties, Trans. Amer. Math. Soc. 350:1 (1998) 1-41.

4) K. A. Kearnes, E. W. Kiss, Finite algebras of finite complexity, Discrete Math. 207:1-3 (1999) 89-135.

5) K. A. Kearnes, E. W. Kiss, M. A. Valeriote, A geometric consequence of residual smallness, Ann. Pure Appl. Logic 99:1-3 (1999) 137-169.

Activity in the scientific community, international relations

reviewer for Mathematical Reviews since 1979

editor of Algebra Universalis (Birkhauser) since 1998.

board of the Bolyai research fellowship: member since 2007.

organizer of the Budapest Erdős Workshop on Tame Congruence Theory;

coauthors from USA, Canada, Germany, Poland, Russia, Hungary;

visiting professor at universities in Germany, Australia, Canada, USA.

Name: György Kiss

Date of birth: 1961

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): Ph.D. (mathematics)

Teaching activity (with list of courses taught so far):

Eötvös University (1987–):

Geometry (for students in mathematics and applied mathematics; lecture, practice)

Finite Geometries (for students in mathematics; lecture)

Discrete and Combinatorial Geometry (for students in mathamatics; lecture)

Applied Geometry (for students in geography; lecture)

University of Szeged (1997– , part time):

Projective Geometry (lecture, practice)

Finite Geometries and Coding Theory (lecture)

Topology (lecture)

Other professional activity:

24 years of teaching experience, more than 20 diploma thesis supervisions,

1 Ph.D. supervision; more than 20 lectures at international conferences;

32 publications;

Up to 5 selected publications from the past 5 years:

1. Kiss, Gy., Marcugini, S., and Pambianco, F.: On blocking sets of inversive planes, J. Comb. Designs 13 (2005), 268-275.

2. Bezdek, K., Böröczky, K., and Kiss, Gy.: Ont he successive illumination parameters of conves bodies, Periodica Math. Hung. 53 (2006), 71-82.

3. Blokhuis, A., Kiss, Gy., Kovács, I., Malnič, A., Marušič, D. and Ruff, J.: Semiovals contained in the union of three concurrent lines, J. Comb. Designs 15 (2007), 491-501.

4. Kiss, Gy.: Small semiovals in PG(2,q), J. Geom. 88 (2008), 110-115.

5. Kiss, Gy.: A survey on semiovals, Contrib. Discrete Math. 3 (2008), 81-95.

The five most important publications:

1. Hirschfeld, J. W. P. and Kiss, Gy.: Tangent sets in finite planes, Discrete Math. 155 (1996), 107-119.

2. Artzy, R. and Kiss, Gy.: Shape-regular polygons in finite planes, J. Geom. 57 (1996), 20-26.

3. Kiss, Gy.: Illumination problems and codes, Periodica Math. Hung. 39 (1999), 65-71.

4. Kiss, Gy.: One-factorization of complete multigraphs and quadrics in PG(2,q), J. Comb. Designs 10 (2002), 139-143.

5. Jagos, I., Kiss, Gy., and Pór, A.: On the intersection of Baer subgeometries of PG(n,q²), Acta Sci. Math. (Szeged) 69 (2003), 419-429.

Activity in the scientific community, international relations

member of the Bolyai Mathematical Society and the American Mathematical Society;

exterior member of the Centre of Computational and Discrete Geometry (University of

Calgary;

coauthors from England, France, Israel, Italy, The Netherlands, Slovenia and South

Africa;

visiting professor at universities in Canada, England, Italy and Slovenia;

Name: Péter Komjáth

Date of birth: 1953

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, full professor

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1997–2000)

Teaching activity (with list of courses taught so far):

Eötvös University (1974– ):

Algebra, number theory, combinatorics, set theory, logic (for students in mathematics; lecture, practice)

BSM (1985– ):

Set theory, logic, graph algorithms, automata theory (lecture)

Other professional activity:

34 years of teaching experience, 15 diploma thesis supervisions,

over 20 lectures at international conferences;

107 publications;

1 book

Up to 5 selected publications from the past 5 years:

1. P. Komjáth, S. Shelah: Finite subgraphs of uncountably chromatic graphs, Journal of Graph Theory, 49(2005), 28-38.

2. M. Foreman, P. Komjáth: The club guessing ideal (commentary on a theorem of Gitik and Shelah), Journal of Math. Logic, 5(2005), 99-147.

3. P. Komjáth, V. Totik: Problems and Theorems in Set Theory, Springer, 2006.

The five most important publications:

1. J. E. Baumgartner, P. Komjath: Boolean algebras in which every chain and antichain is countable, Fundamenta Mathematicae, CXI(1981), 125-131.

2. P. Komjáth: A decomposition theorem for Rⁿ, Proc. Amer. Math. Soc. 120(1994), 921-927.

3. P. Komjáth, A consistency result concerning set mappings, Acta Math. Hung. 64, (1994) 93-99.

4. G. Cherlin, P. Komjáth, There is no universal countable pentagon free graph, Journal of Graph Theory 18 (1994), 337-341.

5. Z. Furedi, P. Komjáth: On the existence of countable universal graphs, Journal of Graph Theory, 25 (1997), 53-58.

Activity in the scientific community, international relations

organizer of ten international conferences;

member and president of various commitees of the Bolyai Mathematical Society;

Name: Géza Kós

Date of birth: 1967

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Bolyai scholarship (2005–2008)

Teaching activity (with list of courses taught so far):

Eötvös University (1991– ):

real analysis (for students in matehmatics; lectures and practice)

real analysis (for students in physics; practice)

complex analyisis (for students in matehmatics; practice)

geometry (for students in matehmatics; practice)

Other professional activity:

17 years of teaching experience;

4 lectures at international conferences;

20 publications;

2 international patents;

Up to 5 selected publications from the past 5 years:

1. Floater M. S., Kós G., Reimers M: Mean value coordinates in 3D, Computer-Aided Geometric Design 22 (2005), 623–631

2. Floater M. S., Hormann K., Kós G.:A general construction of barycentric coordinates over convex polygons, Advances in Computational Mathematics 244 (2006) 311-331.

3. Kós G.: Two Turán type inequalities, Acta Mathematica Hungarica Online first, 2008

4. Károlyi Gy., Keleti T., Kós G., Ruzsa I.:Periodic decomposition of integer valued functions, Acta Mathematica Hungarica Online First, 2007.

The five most important publications:

1. Borwein P., Erdélyi T., Kós G.: Littlewood-type problems on [0,1], Proc. London Math. Soc. 3 (79), 1999, 22–46

2. Kós G., Martin R. R., Várady T.: Methods to recover constant radius rolling ball blends in reverse engineering, Computer Aided Geometric Design 17, No. 2 (2000), 127--160

3. Kós G.: On the constant factor in Vinogradov's Mean Value Theorem, Acta Arithmetica, 97. No. 2 (2001), 99--101

4. Kós, G.: An algorithm to triangulate surfaces in 3D using unorganised point clouds, Computing Suppl 14, May 2001, 219--232

5. loater M. S., Kós G., Reimers M: Mean value coordinates in 3D, Computer-Aided Geometric Design 22 (2005), 623--631

Activity in the scientific community, international relations

member of the Problem Selection Committee of the International Mathematical Olympiad, 2006-

member of the Problem Selection Committee of the International MathematicalCompetition for University Students (IMC), 1998-;

chairman of the jury of the Vojtech Jarnik International Mathematical Competition, 2002-2006;

KöMaL, 1986– ;

Kürschák Competition committee, 1990-;

secretary of the Schweitzer competition committee 1992.

Name: Antal Kováts

Date of birth: 1949

Highest degree (discipline): secondary school teacher of mathematics

Present employer, position: Generali-Providencia Zrt., chief actuary, and Eötvös Loránd University, associate professor

Scientific degree (discipline): CSc, mathematics

Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):

Probability theory, Statistics, Stochastic processes, Life contingencies – 35 years of teaching experience

Other professional activity:

17 years activity as an actuary, chief actuary from 1994

Up to 5 selected publications from the past 5 years:

The five most important publications:

On the generalized Bernstein polynomials. Annales Univ. Sci. Budapest, Sectio Math., 19 (1976), 93-98.

On the deviation of distributions of sums of independent integer valued random variables. In: F. Konecny, J. Mogyoródi, W. Wertz (Eds.) Probability and Statistical Decision Theory (Proceedings of 4th Pannonian Symposium on Math. Stat., Bad Tatzmannsdorf, Austria, 1983). Akadémiai Kiadó, Budapest, 1985, Vol. A, 219-229.

Asymptotic expansions for approximations by generalized Poisson distribution. Annales Univ. Sci. Budapest, Sectio Comp., 7 (1987), 99-102. (in Russian)

Aging properties of certain dependent geometric sums. J. Appl. Probab. 29 (1992) 655–666. (with T. F. Móri)

Aging solutions of certain renewal type equations. In: J. Galambos, I. Kátai (Eds.) Probability Theory and Applications, Essays to the Memory of József Mogyoródi. Kluwer, Dordrecht, 1992, 125–141. (with T. F. Móri)

Activity in the scientific community, international relations:

Hungarian Actuarial Society (HAS), president 2000–2003,

HAS, board member 2003–

Name: János Kristóf

Date of birth: 1953

Highest degree (discipline): diploma in physics

Present employer, position: Eötvös Loránd University, Department of Applied Analysis and Computational Mathematics, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös Loránd University (1978– ):

Analysis (for students in physiscs; practice): 15 years

Analysis (for students in physiscs; lecture): 12 years

Topological vector spaces (for students in mathematics; lecture): 5 years

Banach algebras (for students in mathematics; lecture): 14 years

Geometric functional analysis (for students in mathematics; lecture): 14 years

C*-algebras (for students in mathematics; lecture): 10 years

Harmonic analysis (for students in mathematics; lecture): 14 years

Other professional activity:

30 years of teaching experience, 6 diploma thesis supervisions, 3 Ph.D. thesis supervisions;

17 publications;

Up to 5 selected publications from the past 5 years:

1. A characterization of von Neumann-algebras, Acta Sci. Math., 2006. (submitted)

2. A noncommutative spectral theorem for GW*-algebras, Studia Sci. Math., 2006. (submitted)

3. On the ultraspectrality of GW*-algebras, Acta Sci. Math., 2007-2008 (in preparation)

4. Non-unital GW*-algebras, Studia Sci. Math., 2008 (in preparation)

5. Elements of mathematical analysis, Vols I-IV, 2003-2008, Hungarian online material at address http://www.cs.elte.hu/~krja

The five most important publications:

1. Ortholattis linéarisables, Acta Sci. Math., 49 (1985)

2. C*-norms defined by positive linear forms, Acta Sci. Math., 50 (1986)

3. On the projection lattice of GW*-algebras, Studia Sci. Math., 22 (1987)

4. Commutative GW*-algebras, Acta Sci. Math., 52 (1988)

5. Spectrality in C*-algebras, Acta Sci. Math, 62 (1996)

Activity in the scientific community, international relations

Name: Miklos Laczkovich

Date of birth: 1948

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, professor

Scientific degree (discipline): MHAS

Teaching activity (with list of courses taught so far):

Eötvös University (1971– ):

analysis (for students in mathematics; lecture, practice)

analysis (for students in mathematics education; lecture, practice)

University College London (2001-):

Mathematics in economics (for students in mathematics; lecture)

BSM (1985-86):

Conjecture and proof (lecture, practice)

Other professional activity:

38 years of teaching experience, 20 diploma thesis supervisions, 4 Ph.D. thesis supervisions;

over 30 lectures at international conferences; about 120 publications.

Up to 5 selected publications from the past 5 years:

1. M. Laczkovich, The removal of pi from some undecidable statements involving elementary functions, Proc. Amer. Math. Soc. 131 (2003), no. 7, 2235-2240.

2. M. Laczkovich, Configurations with rational angles and Diophantine trigonometric equations. In: B. Aronov, S. Basu, J. Pach and M. Sharir (Editors): Discrete and Computational Geometry. The Goodman-Pollack Festschrift. Springer 2003, pp. 571-595.

3. M. Laczkovich, Linear functional equations and Shapiro's conjecture, L'Enseignement Math\'ematique 50 (2004), 103-122.

4. M. Laczkovich and L. Szekelyhidi, Spectral synthesis on discrete Abelian groups, Proc. Cambridge Phil. Soc. 143 (2007), 103-120.

5. S. Gao, S. Jackson, M. Laczkovich and R. D. Mauldin, On the unique representation of families of sets, Trans. Amer. Math. Soc. 360 (2008), 939-958.

The five most important publications:

1. M. Laczkovich and D. Preiss, alpha-Variation and transformation into C^n functions, Indiana Univ. Math. J. 34 (1985), 405-424.

2. M. Laczkovich, Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem, J. reine und angew. Math. (Crelle's J.) 404 (1990), 77-117.

3. M. Laczkovich, Uniformly spread discrete sets in R^d , J. London Math. Soc. 46 (1992), 39-57.

4. M. Laczkovich, The difference property. In: Paul Erdos and his Mathematics (editors: G. Halasz, L. Lovasz, M. Simonovits and V. T. Sos), Springer, 2002. Vol. I, 363-410.

5. M. Laczkovich, Paradoxes in measure theory. In: Handbook of Measure Theory (editor: E. Pap), Elsevier, 2002. Vol. I, 83-123.

Activity in the scientific community, international relations

Formal member of the granting committee of the Szechenyi Professor Scholarship;

formal member of the plenum of the Hungarian Accreditation Committee; formal member of the

DSc committee of the HAS, formal member

of the granting committee of the Hungarian NSRF (OTKA).

Head of the Mathematics PhD School of the Eotvos University,

head of the Department of Analysis of the Eotvos University.

Visiting professor at universities in Italy, the UK and the USA.

Name: Gyula Lakos

Date of birth: 1973

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):

Eötvös University (2004– ):

geometry (practice), differential geometry (practice)

differential forms (lecture), general structures in differential geometry (lecture)

Northwestern University(2003–2004):

Linear Algebra, Multivariable Calculus, Differential Equations (lecture, practice)

Massachusetts Institute of Technology(1998–2003):

Multivariable Calculus (recitation), Advanced Mathematical Methods for Engineers (lecture), Summer Program in Undergraduate Research (coordinating mentor)

Other professional activity: 10 years of teaching experience, 7 preprints, several lecture notes

Up to 5 selected publications from the past 5 years:

1. Lakos, Gy.: Notes on Lebesgue integration, lecture notes, arXiv:math.FA/0506185

2. Lakos, Gy.: On the naturality of the Mathai-Quillen formula, to appear in Studia Math. Sci. Hung.

3. Lakos, Gy.: Self-stabilization in certain infinite-dimensional matrix algebras, preprint, arXiv:math.KT/0506059

4. Lakos, Gy.: Spectral calculations on locally convex vector spaces, preprint, arXiv:math.FA/0611171

5. Lakos, Gy.: Factorization of Laurent series over commutative rings, preprint, arXiv:0709.4107

The five most important publications:

1. Lakos, Gy.: Notes on Lebesgue integration, lecture notes, arXiv:math.FA/0506185

2. Lakos, Gy.: On the naturality of the Mathai-Quillen formula, to appear in Studia Math. Sci. Hung.

3. Lakos, Gy.: Self-stabilization in certain infinite-dimensional matrix algebras, preprint, arXiv:math.KT/0506059

4. Lakos, Gy.: Spectral calculations on locally convex vector spaces, preprint, arXiv:math.FA/0611171

5. Lakos, Gy.: Factorization of Laurent series over commutative rings, preprint, arXiv:0709.4107

Activity in the scientific community, international relations

member of the János Bolyai Mathematical Society, (1992–)

Name: László Lovász

Date of birth: 1948

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, professor, director

Scientific degree (discipline): DrSc (mathematics),

Member of the Hungarian Academy of Science: 1979

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1971–75, 1982–):

geometry (for students in mathematics; practice), finite mathematics (for students in mathematics; lecture), combinatorial optimization (for students in mathematics; lecture), complexity of algorithms (for students in mathematics and informatics; lecture), random methods and algorithms (for students in mathematics; lecture), topological methods in combinatorics (for students in mathematics; lecture), algebraic and probabilistic methods in combinatorics (for students in mathematics; lecture)

József Attila University (1975-1982)

geometry (for students in mathematics; lecture and practice), differential geometry (for students in mathematics; lecture), discrete optimization (for students in mathematics; lecture and practice)

Yale University (1993-1999)

introduction to mathematics (lecture), mathematical tools for computer science (lecture)

algorithms (lecture), algebraic methods in combinatorics (lecture), complexity of algorithms (lecture)

BSM (1987– )discrete mathematics (lecture), geometric graph theory (lecture)

Other professional activity:

36 years of teaching experience, 10 Ph.D. thesis supervisions; over 50 lectures at international conferences; 250 research publications; 2 US patents; 20 expository articles

Up to 5 selected publications from the past 5 years:

L. Lovász, B. Szegedy: Limits of dense graph sequences, J. Comb. TheoryB 96 (2006), 933–957.

L. Lovász, K. Vesztergombi, U. Wagner, E. Welzl: Convex quadrilaterals and k-sets, in: Towards a Theory of Geometric Graphs, (J. Pach, Ed.), AMS Contemporary Mathematics 342 (2004), 139–148.

L. Lovász: Graph minor theory, Bull. Amer. Math. Soc. 43 (2006), 75–86.

L. Lovász, M. Freedman, A. Schrijver: Reflection positivity, rank connectivity, and homomorphisms of graphs, J. Amer. Math. Soc.20 (2007), 37–51.

L. Lovász, S. Vempala: Simulated Annealing in Convex Bodies and an O*(n⁴) Volume Algorithm, J. Comput. System Sci. 72 (2006), 392-417.

The five most important publications:

L. Lovász: Normal hypergraphs and the perfect graph conjecture, Discrete Math. 2 (1972), 253-267; reprinted Annals of Discrete Math. 21 (1984) 29-42.

L. Lovász: Kneser’s conjecture, chromatic number, and homotopy, J. Comb. TheoryA 25 (1978), 319-324.

L. Lovász: On the Shannon capacity of graphs, IEEE Trans. Inform. Theory25 (1979), 1-7.

A.K. Lenstra, H.W. Lenstra, L. Lovász: Factoring polynomials with rational coefficients, Math. Annalen261 (1982), 515-534.

L. Lovász: Approximating clique is almost NP-complete (with U. Feige, S. Goldwasser, S. Safra and M. Szegedy), Proc. 32nd IEEE FOCS (1991), 2-12.

Activity in the scientific community, international relations

President of the International Mathematical Union, 2007-; Executive Committee of the International Mathematical Union,

1987-1994. Abel Prize Committee, 2004-2006; Chair, International Bolyai Prize Committee, 2000-2006; Chair, Nevanlinna Prize Committee, 1988-1990; Presiduum of the Hungarian Academy of Sciences, 1990-1993, 2008-;Member, Program Committee of ICM 2002; Editor-in-Chief, Combinatorica, 1981-.

Member of editorial board for 12 other journals: J. Combinatorial Theory (B), Discrete Math., Discrete Applied Math., Geometric and Functional Analysis, J. Graph Theory, Europ. J. Combinatorics, Discrete and Computational Geometry, Random Structures and Algorithms, Electronic Journal of Combinatorics, Acta Mathematica Hungarica, Acta Cybernetica, Természet Világa

Name: András Lukács

Date of birth: 1968

Highest degree (discipline): diploma in mathematics

Present employer, position: Computer and Automation Institute, reserach fellow,

Eötvös Loránd University, reserach fellow

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: OTKA postdoctoral fellowship (2000–2003)-

Teaching activity (with list of courses taught so far):

Numerical analysis (for students in mathematics and in computer science, 1990–1991)

Discrete mathematics (for students in mathematics and in informatics, 1993– )

Combinatorics of set systems (for students in teaching mathematics, 2002)

Complexity theory (for students in computer science, 2003)

Data mining (2003– )

Random walks in graphs (1995)

Combinatorial probability theory (2001)

Other professional activity:

Over 8 years of teaching experience

Guest reseracher in several universities (Univ. Köln, Inst. für Informatik, 1992-1993,

Montanuniv. Leoben, Inst. für Ang. Math., 1994-1995, CWI Amsterdam, 1998-2000)

Research position in the Research Laboratory of the Computer and Automation Institute (1995– )

Up to 5 selected publications from the past 5 years:

Bounded contraction of graphs with polynomial growth (with N. Seifter), European Journal of Combinatorics 22 (1) (2001), no. 1, 85-90. (IF=0,335)

High density compression of log files (with B. Rácz), Proceedings of the Data Compression Conference 2004, Snowbird, UT, USA. IEEE Computer Society

Generating random elements of abelian groups, Random Structures and Algorithms, várhatóan 2005. (IF=0,759)

The five most important publications:

Lattices in graphs with polynomial growth (with N. Seifter), Discrete Math. 186 (1998), no. 1-3, 227-236. (IF=0,301)

On local expansion of vertex-transitive graphs, Combin. Probab. Comput. 7 (1998), no. 2, 205-209. (IF=0,512)

Bounded contraction of graphs with polynomial growth (with N. Seifter), European Journal of Combinatorics 22 (1) (2001), no. 1, 85-90. (IF=0,335)

Approximate representation of groups (2004) (with László Babai and Katalin Friedl) (kézirat) Generating random elements of abelian groups, Random Structures and Algorithms, várhatóan 2005. (IF=0,759)

Activity in the scientific community, international relations

member of the Bolyai Mathematical Society (1993– ), Institute of Combinatorics and its Applications (1995– ),

technical editor of Combinatorica (996–1998)

member of the organizing committee of the 2nd European Congress of Mathematics (1996)

Internatonal relations: CWI Amsterdam, Cambridge Univ., Montanuniv. Leoben.

Name: Gergely Mádi-Nagy

Date of birth: 1973

Highest degree (discipline): diploma in mathematics, BSc in economics

Present employer, position: BUTE, assistant professor, Eötvös University, part-time assistant professor

Scientific degree (discipline): PhD (applied mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1997– ):

Operations Research, Decision Theory, Nonlinear Programming

BUTE (2000– )

Calculus, Linear Algebra, Operations Research, Probability Theory, Statistics

Other professional activity:

10 years of teaching experience, 1 National Student Research Conference (OTDK) supervisions (2nd place), 10 talks at international conferences, seminars;

5 refereed publications; 6 research reports;

Up to 5 selected publications from the past 5 years:

Prékopa, A. and G. Mádi-Nagy (2008). A Class of Multiattribute Utility Functions. Economic Theory, 34 (3), pp. 591-602

Mádi-Nagy, G. (2005). A method to find the best bounds in a multivariate discrete moment problem if the basis structure is given. Studia Scientiarum Mathematicarum Hungarica 42 (2), pp. 207 - 226.

Mádi-Nagy, G. and A. Prékopa (2004).On Multivariate Discrete Moment Problems and their Applications to Bounding Expectations and Probabilities. Mathematics of Operations Research 29(2), pp. 229-258.

Mádi-Nagy G. és Prékopa A. (2004). Egy többváltozós hasznossági függvény. (A Mulitivariate Utility Function, with english abstract) Alkalmazott Matematikai Lapok 21, 23-34.

The five most important publications:

Prékopa, A. and G. Mádi-Nagy (2007). A Class of Multiattribute Utility Functions. Economic Theory, 34 (3), pp. 591-602

Mádi-Nagy, G. (2005). A method to find the best bounds in a multivariate discrete moment problem if the basis structure is given. Studia Scientiarum Mathematicarum Hungarica 42 (2), pp. 207 - 226.

Mádi-Nagy G. és Prékopa A. (2004). Egy többváltozós hasznossági függvény. (A Mulitivariate Utility Function, with english abstract) Alkalmazott Matematikai Lapok 21, 23-34.

Nagy G. és Prékopa A. (2000). Többváltozós diszkrét függvények féloldalas approximációja polinomokkal. (One-sided Approximation of Multivariate Discrete Functions by Polynomials, with english abstract) Alkalmazott Matematikai Lapok 20, 195-215.

Activity in the scientific community, international relations

member of Hungarian Operations Research Society

coauthors from USA;

visiting reseracher at universities in Germany, USA;

Name: László Márkus

Date of birth: 1961

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Loránd University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):

Eötvös University (1990- ):

Time Series Analysis (lecture, for students in mathematics/applied mathematics)

Spectral and Parameter estimation of Stochastic Processes(lecture, for students in mathematics)

Analysis of financial processes I-II. (lecture, for students in mathematics/applied mathematics)

Probability Theory (practice/tutorial, for students in mathematics/applied mathematics)

Mathematical Statistics (practice/tutorial, for students in mathematics/applied mathematics)

Advanced Probability Theory (lecture, for students in informatics)

Advanced Mathematical Statistics (lecture, for students in informatics)

Probability Theory (lecture, for students in geophysics; astronomy;)

Mathematical Statistics (lecture, for students in geophysics, astronomy; )

Other professional activities in the last 5 years:

18 years of teaching experience,

12 diploma thesis supervisions, supervision of the work of 4 Ph.D. students

Over 30 lectures at international conferences; 32 publications, 18 of them in peer reviewed journals;

2000 - 2003: Head of an international thematic research project, funded by the Hungarian National Scientific Research Fund (OTKA) (10 participants, of them two British, two German).

2001-2004: Co-ordinator of time series modelling in a National Research and Development Project for estimating flood risks of Tisza River2002-2004: Participant in the PRO-ENBIS project of the EU for establishing the European Network for Business and Industrial Statistics (ENBIS).

2004 - 2007: Head of an international thematic research project: funded by the Hungarian National Scientific Research Fund (OTKA) (12 participants, of them two British, one German-Canadian).

2005-2007: Research projects at Eötvös University funded by different international insurance companies. Co-ordinator of 3 of those projects Participant in 3 further projects.

Up to 5 selected publications from the past 5 years:

László Márkus, Péter Elek: A long range dependent model with nonlinear innovations for simulating daily river flows, Natural Hazards in Earth System Sciences, 2004., Vol.2., pp.277-283.

László Márkus, József Kovács, Gábor Halupka: Dynamic Factor Analysis for Quantifying Aquifer Vulnerability, Acta Geologica Hungarica, 2004. Vol. 47. No.1. pp.1-17.

Ian Dryden, László Márkus, Charles Taylor, József Kovács: Non-Stationary spatio-temporal analysis of karst water levels Journal of the Royal Statistical Society, Series C-Applied Statistics 2005.,Vol.54., No.3., pp. 673-690.

Péter Elek, László Márkus: A light-tailed conditionally heteroscedastic model with applications to river flows, Journal of Time Series Analysis, 2008. Vol. 29, No.1, 14-36.

Krisztina Vasas, Péter Elek, László Márkus: A two state regime switching autoregressive model with application to river flow analysis, Journal of Statistical Planning and Inference, 137 (2007) pp. 3113 - 3126.

The five most important publications:

László Márkus: On a stability problem of the forecast of Lévy's Brownian motion, Probability Theory and Its Applications, 1997. Vol. 42., No. 2, pp.407-409.

László Márkus, Olaf Berke, József Kovács and Wolfgang Urfer Spatial Prediction of the Intensity of Latent Effects Governing Hydrogeological Phenomena Environmetrics, 1999. Vol 10. pp. 633-654.

Péter Elek, László Márkus: A light-tailed conditionally heteroscedastic model with applications to river flows, Journal of Time Series Analysis, 2008. Vol. 29, No.1, 14-36.

Activity in the scientific community, international relations

Membership in Scientific Organisations:

Bernoulli Society for Probability Theory and Statistics 1990-present

European Regional Committee of the Bernoulli Society elected member for 2008-2012

INTECOL - Society for International Ecological Sciences1998-present

EGU - European Geological Union 1997-2005

The Applied Stochastic Models and Data Analysis International Society 2006-present

RefeRee for the journals: Journal of Time Series Analysis, Water Resources Research

organizer of two international conferences

Name: György Michaletzky

Date of birth: 1950

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, professor, head of department

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1997–2001)

Teaching activity (with list of courses taught so far):

Probability Theory, Statistics, Multidimensional statistical analysis, Stochastic processes, control and filtering, Stochastic differential equations, Birth and death processes, Queueing systems, Stationary stochastic processes, Risk processes, Markov-processes, Distribution of the eigenvalues of random matrices, Hankel-approximation, Sampling theory, System theory.

Other professional activity:

33 years of teaching experience, over 30 lectures at international conferences;

53 publications

Up to 5 selected publications from the past 5 years:

~, Quasi-similarity of compressed shift operators, Acta Sci. Math., Szeged, 69(2003), 223-239

~, Kockázati folyamatok, Eötvös Kiadó, Jegyzet, 2. átdolgozott kiadás, 2001.

~, L. Gerencsér, BIBO--stability of switching systems, IEEE Trans. on Automatic Control, 47/11, 2002, 1895-1898.

I. Gyöngy – ~, On the Wong-Zakai approximations with delta martingales,

Proc. R. Soc. London, A. 460(2003), 309-324.

L. Gerencsér, ~ , Zs. Vágó, Risk sensitive identification of linear stochastic systems, accepted Mathematics of Control, Signals and Systems 17 (2005), 77-100.

The five most important publications:

A. Lindquist, Gy. Michaletzky – G. Picci, Zeros of spectral factors, the geometry of splitting subspaces, and the algebraic Riccati inequality, SIAM J. Control, Vol. 33. No. 2. pp. 365-401, 1995.

Gy. Michaletzky, J. Bokor, P. Várlaki, Representability of Stochastic Systems, Akadémiai Kiadó, 1998.

Gy. Michaletzky – A. Ferrante, Splitting subspaces and acausal spectral factors, J. Math. Systems, Estim. and Control Vol. 5. No. 3.pp.363-366, 1995.

A. Lindquist – Gy. Michaletzky, Output-induced subspaces, invariant directions and interpolation in linear discrete time stochastic systems, SIAM J. Control, 35/3 pp.810-859, 1997.

M. Bolla - Gy. Michaletzky - G. Tusnády - M. Ziermann, Extrema of sums of heterogeneous quadratic forms, Linear Algebra and Applic. 269 1998, 331-365.

Activity in the scientific community, international relations

Name: Tamás F. Móri

Date of birth: 1953

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Loránd University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Széchenyi Professor scholarship (1998–2001)

Teaching activity (with list of courses taught so far):

Eötvös Loránd University (1978– ):

Probability theory (for students in mathematics, applied mathematics, and informatics; lecture, practice)

Mathematical statistics (for students in mathematics, applied mathematics, informatics, and geophysics; lecture, practice)

Stochastics (for students in mathematics; lecture)

Foundations of statistics 1-2 (for students in mathematics, and applied mathematics; lecture)

Discrete parameter martingales (for students in mathematics; lecture)

Analysis of survival data (for students in mathematics, and applied mathematics; lecture)

Measure and integral (in English, for MSc students)

Advanced probability theory (in English, for MSc students)

Foundations of statistics (in English, for MSc students)

Analysis of survival data (in English, for MSc students)

Other professional activity:

30 years of teaching experience, 14 diploma thesis supervisions, 2 PhD thesis supervisions.

Textbooks, lecture notes (in Hungarian):

Multivariate Statistical Analysis (Műszaki Könyvkiadó, Budapest, 1986), Editor

Teaching software for PC in mathematics (complex function theory), also in English and German, 1987–90

Mathematical statistics (Tankönyvkiadó, Budapest, 1995), Ch.II. Estimations

Problem book in mathematical statistics (ELTE Eötvös Kiadó, Budapest, 1997) (with L. Szeidl and A. Zempléni)

Discrete parameter martingales (ELTE, 1999)

Analysis of survival data. Available online http://www.math.elte.hu/~mori/elettartam.pdf

Activities in other institutions, visits:

1985-1991 Research fellow, Mathematical Institute of the HAS

2006-2010 Associated member, Alfréd Rényi Institute of Mathematics

1992 University of Sheffield, Department of Probability and Statistics, one month visit, TEMPUS individual mobility grant

Up to 5 selected publications from the past 5 years:

Almost sure convergence of weighted partial sums. Acta Math. Hungar., 99 (2003), 285–303. (with B. Székely)

The maximum degree of the Barabási random tree. Comb. Probab. Computing, 13 (2004)

The convexity method of proving moment–type inequalities. Statist. Probab. Lett., 66 (2004), 303–313. (with V. Csiszár)

A new class of scale free random graphs. Statist. Probab. Lett.76 (2006), 1587–1593. (with Z. Katona)

Degree distribution nearby the origin of a preferential attachment graph. Electron. Comm. Probab., 12 (2007), 276–282.

The five most important publications:

On the rate of convergence in the martingale central limit theorem. Studia Sci. Math. Hungar. 12 (1977) 413–417.

Asymptotic behaviour of symmetric polynomial statistics. Ann. Probab. 10 (1982) 124–131. (with G. J. Székely)

A note on the background of several Bonferroni–Galambos type inequalities. J. Appl. Probab. 22 (1985) 836–843. (with G. J. Székely)

On the waiting time till each of some given patterns occurs as a run. Probab. Th. Rel. Fields 87 (1991) 313–323.

Covering with blocks in the non-symmetric case. J. Theor. Probab. 8 (1995) 139–164.

Activity in the scientific community, international relations:

1979– member of the J. Bolyai Mathematical Society, 2006–2009 secretary of the Ethical Committee

1979– member of the Bernoulli Society for Probability Theory and Mathematical Statistics, 2000–2004 member of the European Regional Committee

2002–2005 member of the mathematical jury of OTKA

Name: Gábor Moussong

Date of birth: 1957

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Eötvös University (1982– ):

geometry, differential geometry, topology, algebraic topology (for students in mathematics, lecture, practice)

mathematics (for students in cartography; lecture)

Universiteit Gent (1991):

algebraic topology (for students in mathematics, lecture)

BSM (1997– )

topics in geometry (lecture, practice)

The Ohio State University (1997-1998):

calculus and analytic geometry

topics in geometry

Other professional activity:

26 years of teaching experience, 20 diploma thesis supervisions;

over 15 lectures at international conferences;

11 publications;

Up to 5 selected publications from the past 5 years:

1. Moussong, G., Prassidis, S.: Equivariant rigidity theorems, New York J. Math. 10 (2004),
151-167.

2. Moussong, G.: Models of hyperbolic geometry, in: Bolyai memorial volume, ed. by K. Kapitány, G. Németh, V. Silberer, Vince Kiadó (2004), 143-165 (in Hungarian).

3. Csikós, B., Moussong, G.: On the Kneser-Poulsen Conjecture in Elliptic Space, Manuscripta Math., 121 (2006), 481-489.

The five most important publications:

1. Moussong, G.: Hyperbolic Coxeter Groups, Ph.D. Dissertation, The Ohio State University, 1988.

2. Moussong, G.: Some non-symmetric manifolds. Differential geometry and its applications, Coll. Math. Soc. J. Bolyai 56, North Holland, Amsterdam (1992), 535-546.

3. Charney, R., Davis, M. W., Moussong, G.: Nonpositively curved, piecewise Euclidean structures on hyperbolic manifolds, Michigan Math. J. 44 (1997) no. 1., 201-208.

4. Davis, M. W., Moussong, G.: Notes on Nonpositively Curved Polyhedra. Low Dimensional Topology, eds. K. Böröczky Jr., W. Neumann, A. Stipsicz, Bolyai Society Math. Studies Nr. 8 (1999), 11-94.

5. Moussong, G., Prassidis, S.: Equivariant rigidity theorems, New York J. Math. 10 (2004), 151-167.

Activity in the scientific community, international relations

member of the Bolyai Mathematical Society, 1982– ;

organizer of five international conferences;

member of editorial board for Periodica Math. Hung., 1991-1997;

committee member for the National Mathematical Competition for Secondary Schools, 1990-;

program manager for Budapest Semesters in Mathematics, 1989-1991;

coauthors from USA;

visiting professor at universities in Belgium, USA.

Name: András Némethi

Date of birth: 1959

Highest degree (discipline): diploma in mathematics

Present employer, position: Alfréd Rényi Institute of Mathematics, researcher

Scientific degree (discipline): Doctor of Science (mathematics)

Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):

OSU Columbus, Ohio, USA (1991–2006):

Algebra, Geometry, Analysis, Algebraic Geometry, Algebraic Topology

CEU (2004– )

Algebraic Geometry, Hodge Theory

Other professional activity:

1985-1990, Researcher, National Institute for Science and Technical Research, Bucharest, Romania.

1991-1995, Instructor, Ohio State University, USA

1995-1998, Assistant Professor, Ohio State University, USA

1998-2002, Associate Professor, Ohio State University, USA

2002-2006, Professor, Ohio State University, USA

2004 óta, Researcher, Alfréd Rényi Institute of Mathematics, Budapest (head of the Algebraic Geometry and Differential Topology research division).

Up to 5 selected publications from the past 5 years:

1. Némethi, A.: Invariants of normal surface singularities, Contemporary Mathematics, 354 (2004), 161-208.

2. Mendris, R. and Némethi, A.: The link of f(x,y)+zⁿ=0 and Zariski’s Conjecture, Compositio Math., 141 (2005), 502-524.

3. Némethi, A.: On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds, Geometry and Topology, 9 (2005), 873-883.

4. McNeal, J.D., Némethi, A.: The order of contact of a holomorphic ideal in C², Math. Zeitschrift, 250(4) (2005), 873-883

5. J.F. de Bobadilla, Luengo, I., Melle-Hernández, A. and Némethi, A.: On rational cuspidal projective plane curves, Proc. of London Math. Society, 92 (2006), 99-138.

The five most important publications:

1. Némethi, A. and Steenbrink, J.: Extended Hodge bundles for Abelian, Annals of

Mathematics, 143 (1996), 131-148.

2. Némethi, A.: ``Weakly” Elliptic Gorenstein singularities of surfaces, Inventiones Math., 137 (1999), 145-167.

3. Némethi, A. and Nicolaescu, L.I.: Seiberg-Witten invariants and surface singularities,

Geometry and Topology, 6 (2002), 269-328.

4. Némethi, A.: On the Heegaard Floer homology of S³_-d(K) and unicuspidal rational plane

curves, Fields Institute Communications, 47 (2005), 219-234.

5. Luengo, I., Melle-Hernández, A. and Némethi, A.: Links and analytic invariants of

superisolated singularities, Journal of Algebraic Geometry, 14 (2005), 543-565.

Activity in the scientific community, international relations

Editor of the journals Periodica Mathematica Hungarica and

Studia Scientiarium Math. Hungarica;

Organizer of eight international conferences;

Visiting positions at

– Math. Inst. of the Hungarian Academy of Sciences, Budapest, Hungary (March 1990-

May 1990)

– University of Utrecht and Nijmegen, the Netherlands (Sept. 1990-Dec. 1990)

– University of Toronto, Canada (July 1991)
– MSRI, Berkeley (May 1993)
– University of Nice, France (July 1993)
– University of Nijmegen, the Netherlands (Sept. 1993-June 1994)
– E´cole Polytechnique, Palaiseau, France (Oct. 1996-Dec. 1996)
– University of Nice, France (June 15-July 15, 1997)
– University of Nantes, France (June 01-30, 1998)
– University of Bordeaux, France (November 01-30, 1999)
– Rényi Institute of Mathematics, Budapest, Hungary (July 1999-June 2000)
– University of Hannover, Germany (October 01-30, 2005).

Coauthors from several countries;

Name: Péter P. Pálfy

Date of birth: 1955

Highest degree (discipline): diploma in mathematics

Present employer, position: Alfréd Rényi Institute of Mathematics, director;

Eötvös University, professor

Scientific degree (discipline): DSc (mathematics),

corresponding member of the Hungarian Academy of Sciences (2004)

Major Hungarian scholarships: Széchenyi professor’s scholarship (1998–2001)

Teaching activity (with list of courses taught so far):

Eötvös University (1978– ):

Algebra, Algebra and number theory, Linear algebra, Group theory, Lie algebras, Lattice theory, Permutation groups, Simple groups of Lie type, Group representation theory, Seminar in algebra

Vanderbilt University (1983):

Linear algebra, Group theoretic methods in universal algebra

University of Hawaii (1986):

Caluculus III, Probability theory

Technische Hochschule Darmstadt (1991-1992):

Lineare Algebra, Gruppentheorie

Other professional activity:

30 years of teaching experience, 8 diploma thesis supervisions, 2 Ph.D. thesis supervisions;

over 80 lectures at international conferences;

57 publications;

Up to 5 selected publications from the past 5 years:

1. C.H. Li, Z.P. Lu, P.P. Pálfy, Further restrictions on the structure of finite CI-groups, J. Algebraic Comb. 26 (2007), 161-181.

2. P.P. Pálfy, Maximal clones and maximal permutation groups, Discuss. Math. Gen. Algebra Appl. 27 (2007), 277-291.

3. P.P. Pálfy, A non-power-hereditary congruence lattice representation of M3, Publ. Math. Debrecen 69 (2006), 361-366.

4. P. Hegedűs, P.P. Pálfy, Finite modular congruence lattices, Algebra Universalis 54 (2005), 105-120.

5. P.P. Pálfy, Groups and lattices, London Math. Soc. LNS vol. 305, 428-454.

The five most important publications:

1. P.P. Pálfy, Isomorphism problem for relational structures with a cyclic automorphism, Europ. J. Combinatorics 8 (1987), 35-43.

2. P.P. Pálfy, Unary polynomials in algebras, I, Algebra Universalis 18 (1984), 262-273.

3. L. Babai, P.J. Cameron, P.P. Pálfy, On the orders of primitive groups with restricted composition factors, J. Algebra 79 (1982), 161-168.

4. P.P. Pálfy, A polynomial bound for the orders of primitive solvable groups, J. Algebra 77 (1982), 127-137.

5. P.P. Pálfy, P. Pudlák, Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups, Algebra Universalis 11 (1980), 22-27.

Activity in the scientific community, international relations

Mathematics committee of the Hungarian Academy of Sciences: member since 1985, secretary 1990-1996, chairman since 2005;Board of the Bolyai research fellowship: member 2004-2006, chairman since 2007;

chairman of the mathematics granting committee of the Hungarian NSRF (OTKA), 2001–2003;

member of the Hungarian Accreditation Committee (1997-2000 and 2007-);

member of the Scientific Council of the International Banach Center (Warsaw) since 2006;

member of the committee for the Bolyai prize (2007);

editor-in-chief of Studia Scientiarum Mathematicarum Hungarica (since 2007)

coauthors from Czechoslovakia, England, USA, Australia, China;

visiting professor at Vanderbilt University (USA, 1983), the University of Hawaii (USA, 1986) and Technische Hochschule Darmstadt (Germany, 1991-1992).

Name: Katalin Pappné Kovács

Date of birth: 1955

Highest degree (discipline): diploma in mathematical education

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Teaching activity (with list of courses taught so far):

Eötvös University (1987– ):

algebra (for students in mathematics; lecture, practice)

number theory (for students in mathematics; lecture, practice)

linear algebra (for student in informatics; practice)

algebra and number theory, teaching algebra and number theory (for PhD students of the Math. Education PhD program of the University of Debrecen)

University of Illinois (1993–1995 )

linear algebra, differential equation (lecture, practice)

Other professional activity:

32 diploma thesis supervisions;

over 10 lectures at international conferences;

27 publications

Up to 5 selected publications from the past 5 years:

1. On the characterization of n-polyadditive functions, Publ. Math. Debrecen, 2006 (1-7)

2. On triples of consecutive integers, Annales Univ. Sci. 49 (2007), 143-147

The five most important publications:

1. On the characterization of additive functions with monotonic norm, Journal of Number Theory, Vol 24, no.3, 1986, 298-304

2. On a conjecture concerning additive arithmetical functions II, Publ. Math. Debrecen 50, 1997, 1-3

3. On the haracterization of additive functions on Gaussian integers, Publ. Math. Debrecen 58 (1-2) (2001), 73-78

4. On the characterization of n-polyadditive functions, Publ. Math. Debrecen, 2006 (1-7)

5. On triples of consecutive integers, Annales Univ. Sci. 49 (2007), 143-147

Activity in the scientific community, international relations

Bolyai János Math. Society membership

MR-reviewer (for 15 years)

Name: József Pelikán

Date of birth: 1947

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): doctoral degree with distinction (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1969– ):

algebra and number theory (for students in mathematics; lecture, practice) introductory courses,

various topics in algebra (for students in mathematics; lecture) advanced courses

BSM (1988– )

various algebra and number theory courses

short courses in various foreign universities (in English, French and German)

Other professional activity:

39 years of teaching experience, over 10 diploma thesis supervisions; over 10 lectures at international conferences;

16 publications;

Up to 5 selected publications from the past 5 years:

1. Discrete Mathematics. Springer, New York, 2003., x+290 pp., ISBN: 0-387-95584-4 (co-authors: L. Lovász, K. Vesztergombi)

2. On the running time of the Adleman-Pomerance-Rumely primality test. Publ. Math. Debrecen 56 (2000) 523-534. (co-authors: J. Printz, E. Szemerédi)

The five most important publications:

1. Discrete Mathematics. Springer, New York, 2003., x+290 pp., ISBN: 0-387-95584-4 (co-authors: L. Lovász, K. Vesztergombi)

2, Finite groups with few non-linear irreducible characters. Acta Math. Acad. Sci. Hungar. 25 (1974), 223-226.

3, On semigroups, in which products are equal to one of the factors. Period. Math. Hungar. 4 (1973), 103-106.

4, Properties of balanced incomplete block designs. Combin. Theory and its Appl. (Proc. Colloq. Balatonfüred, 1969) vol. III. 869-889., North- Holland, Amsterdam, 1970.

5, Valency conditions for the existence of certain subgraphs. Theory of Graphs (Proc. Colloq. Tihany, 1966) 251-258., Academic Press, New York, 1968.

Activity in the scientific community, international relations

Various leading positions in the János Bolyai Mathematical Society

Member of Board of Editors of Matematikai Lapok

Leader of the Hungarian team at the International Mathematical Olympiad (IMO), 1988–

Member of the Advisory Board of the IMO (since 1992),

Chairman of the Advisory Board of the IMO (since 2002)

Name: Tamás Pfeil

Date of birth: 1967

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: -

Teaching activity (with list of courses taught so far):

Eötvös University (1989– ):

mathematics (for students in biology; lecture, practice)

analysis (for students in mathematics and meteorology; practice)

partial differential equations (for students in mathematics and meteorology; practice)

ordinary differential equations (for students in mathematics; practice)

Other professional activity:

18 years of teaching experience, 1 diploma thesis supervision, lecture and poster at international conferences;

7 publications;

Up to 5 selected publications from the past 5 years:

Pfeil, T., Shape-preserving signal forms in heat conduction, Appl. Math. Modelling, 32 (2008), 1599-1606.

The five most important publications:

1. Faragó, I., Haroten, H., Komáromi, N., Pfeil, T., A hővezetési egyenlet és numerikus megoldásának kvalitatív tulajdonságai. I. A másodfokú közelítés nemnegativitása, a mximum elv és az oszcillációmentesség, Alk. Mat. Lapok, 17 (1993), 123-141.

2. Faragó, I., Haroten, H., Komáromi, N., Pfeil, T., A hővezetési egyenlet és numerikus megoldásának kvalitatív tulajdonságai. I. Az elsőfokú közelítések nemnegativitása, Alk. Mat. Lapok, 17 (1993), 101-121.

3. Pfeil, T., On the time-monotonicity of the solutions of linear second order homogeneous parabolic equations, Annales Univ. Sci. Budapest., 36 (1993), 139-146.

4. Pfeil, T., An elementary proof for the time-monotonicity of the solutions of linear parabolic equations, Publ. Math. Debrecen, 46 (1995), 71-77.

5. Faragó, I., Pfeil, T., Preserving concavity in initial-boundary value problems of parabolic type and its numerical solution, Per. Math. Hungar., 30 (1995), 135-139.

Activity in the scientific community, international relations

member of the committee of Arany Dániel competition of the Bolyai Mathematical Society;

Name: Vilmos Prokaj

Date of birth: 1966

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Bolyai scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Eötvös University:

Analysis 1993-1997 (for students in mathematics; practice)

Functional analysis 1996-1997 (for students in mathematics; practice)

Probability and statistics 1991-1993, 1997-,(for students in mathematics, informatics; practice)

Stochastic processes 2001-, (for students in mathematics; practice)

Stochastic analysis, Stochastic dinamical systems, Filtering of stochastic processes, Reinsurance 2000-, (for students in mathematics; lecture)

Other professional activity:

15 years of teaching experience, 4 diploma thesis supervisions;

12 publications;

Up to 5 selected publications from the past 5 years:

1. A characterization of singular measures. Real Anal. Exchange 29 (2003/04), no. 2, 805--812.

The five most important publications:

1. A characterization of singular measures. Real Anal. Exchange 29 (2003/04), no. 2, 805--812.

2. On a construction of J. Tkadlec concerning sigma-porous sets. Real Anal. Exchange, 27(1):269 273, 2001/02.

3. Márton Elekes, Tamás Keleti, and Vilmos Prokaj.

The composition of derivatives has a fixed point. Real Anal. Exchange, 27(1):131 140, 2001/02.

4. Monotone and discrete limits of continuous functions. Real Anal. Exchange, 25(2):879 885, 1999/00.

5. Restrictions of self-adjoint partial isometries. Period. Math. Hungar., 35(3):211 214, 1997.

Activity in the scientific community, international relations

member of the Bolyai Mathematical Society;

Name: Tamás Pröhle

Date of birth: 1952

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Loránd University, assistant

Scientific degree (discipline): –

Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):

Application of multivariate statistical methods

Statistical computing

Probability theory and statistics

– more than 25 years of teaching experience

Other professional activity: In connection with statistical computing. Main field of interest includes statistical analysis of multivariate data and time series. Prepared teaching materials for statistical softwares such as SPSS, SAS, and MATLAB. Applies mathematical statistics in a wide range of fields in science, law, and technology (environmental management, hydrology, psychology, jurisdiction, medicine, anthropology, design of experiments etc.)

Up to 5 selected publications from the past 5 years:

I. László, T. Pröhle et al.: A Method for Clustering Satellite Images Using Segments, Annales Univ. Sci. Budapest, Sect. Comp. 23 (2004), 163-178.

The five most important publications:

I. László, T. Pröhle et al.: A Method for Clustering Satellite Images Using Segments, Annales Univ. Sci. Budapest, Sect. Comp. 23 (2004), 163-178.

Gy. Gyenis, T. Pröhle et al.: Body Composition in Puberty Period, In: Puberty: Variabiliy of Changes and Complexity of Factors, Eötvös Univ. Press, Budapest 2000, pp 75-82.

B. Rojkovich, T. Pröhle et al.: Urinary excretion of thial components in patient with rheumatoid arthritis. Clin. Diagn. Lab. Immunol. 1999, 6, 683-685.

Activity in the scientific community, international relations:

Member of the Hungarian Association for Image Analysis and Pattern Recognition, and of the John von Neumann Computer Society. Active member of Users Groups of several statistical software packages (MATLAB, SPSS, SAS, STATISTICA), where he regularly holds lectures.

Name: András Recski

Date of birth: 1948

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, professor (part time) and

Budapest University of Technology and Economics, professor (full time)

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (2000–2004)

Teaching activity (with list of courses taught so far):

Eötvös University (1972– ):

algebra (for students in mathematics; lecture, practice)

discrete mathematics (for students in mathematics and informatics)

Budapest University of Technology and Economics (1990– )

analysis and discrete mathematics (for students in electrical engineering

and informatics; lecture, practice)

Other professional activities:

36 years of teaching experience, about 6 diploma thesis supervisions,

5 Ph.D. thesis supervisions; over 70 lectures at international conferences;

approx. 110 publications.

Up to 5 selected publications from the past 5 years:

1. T. Jordán – A. Recski – D. Szeszlér: System optimization, Typotex, Budapest, 2004.

2. A. Recski: Maps of matroids with applications, Discrete Math. 303 (2005) 175-185.

3. A. Recski – D. Szeszlér: The evolution of an idea – Gallai’s algorithm, Bolyai Soc. Math. Studies 15 (2006) 317-328.

4. A. Recski – J. Szabó: On the generalization of the matroid parity problem, Graph Theory, Trends in Mathematics, Birkhauser, 2006, 347-354.

5. K. Friedl – A. Recski – G. Simonyi: Graph theory exercises, Typotex, Budapest, 2006.

The five most important publications:

1. L. Lovász – A. Recski: On the sum of matroids, Acta Math. Acad. Sci. Hungar. 24 (1972) 329-333.

2. M. Iri – A. Recski: What does duality really mean? Circuit Th. Appl. 8 (1980) 317-324.

3. A. Recski: Matroid theory and its applications in electric engineering and in statics, Springer, Berlin, 1989.

4. A. Recski: Combinatorics in electric engineering and statics, Handbook of Combinatorics, Elsevier, Amsterdam, 1995, 1911-1924.

5. A. Recski: Some polynomially solvable subcases of the detailed routing problem in VLSI design, Discrete Applied Math. 115 (2001) 199-208.

Activity in the scientific community, international relations

member of the editorial board of 5 math journals;

organizer of several international conferences;

general secretary of the János Bolyai Mathematical Society;

Name: András Sárközy

Date of birth: 1941

Highest degree (discipline): diploma in mathematics (1963)

Present employer, position: Eötvös University, professor

Scientific degree (discipline): DSc (mathematics), 1982;

regular member of the Hungarian Academy of Sciences, 2004

Major Hungarian Scholarships: Széchenyi Professor’s Scholarship (1999-2002)

Teaching activity:

Eötvös University (1963– ):

algebra, number theory, algebra and number theory, computational number theory, linear algebra, combinatorial number theory, applications of exponential sums in number theory, additive number theory

University of Illinois (1972/73, 1989/90), UCLA (1983), University of Georgia (1985/1986), The City University of New York, Baruch College (1986/1987), University of Waterloo (1990/91), The University of Memphis (2007/2008):

calculus, linear algebra, linear programming, complex analysis, algebraic number theory, combinatorial number theory, elementary analytical number theory

Other professional activity:

researcher: Rényi Institute (1971-1994), 6 years in USA, Canada, France, Germany, England

220 research papers and 4 books

5 selected publications from the past 5 years:

1. L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory 106 (2004), 56-69.

2. R. Ahlswede, L. Khachatrian and A. Sárközy, On the density of primitive sets, J. Number Theory 109 (2004), 319-361.

3. C. Mauduit and A. Sárközy, Construction of pseudorandom binary sequences by using the multiplicative inverse, Acta Math. Hungar. 108 (2005), 239-252.

4. A. Sárközy, On sums and products of residues modulo p, Acta Arith. 118 (2005), 403-409.

5. P. Hubert, C. Mauduit and A. Sárközy, On pseudorandom binary lattices, Acta Arith. 125 (2006), 51-62.

A tudományos életmű szempontjából legfontosabb 5 publikáció:

1. A. Sárközy, On difference sets of sequences of integers, 1, Acta Math. Acad. Sci. Hungar. 31 (1978), 125-149.

2. A. Sárközy, On divisors of binomial coefficients, 1., J. Number Theory 20 (1985), 70-80.

3. A. Sárközy and C. L. Stewart, On divisors of sums of integers, II, l. Reine Angew. Math. 365 (1986), 171-191.

4. A. Sárközy, Finite addition theorems, II., J. Number Theory 48 (1994),197-218.

5. C. Mauduit and A. Sárközy, On finite pseudorandom binary sequences, 1, Measure of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), 365-377.

Activity in the scientific community, international relations

President of the Mathematical Committee of the Hungarian Academy of Sciences (2003-2006)

President of the mathematical jury of the HNFSR (OTKA), 1999-2001

Editor of 5 mathematical journals

Visiting professor, resp. researcher in USA, Canada, UK, Germany and France for altogether 11 years

56 coauthors from 10 countries

Name: Zoltán Sebestyén

Date of birth: 1943

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, Institute of Mathematics, full professor

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1997–2001)

Teaching activity (with list of courses taught so far):

Eötvös University (1967– ):

analysis(for students in mathematics, physic, geophysic, chemistry; lecture, practice)

functional analysis (for students in mathematics; lecture, practice)

Other professional activity:

40 years of teaching experience, 20 diploma thesis supervisions, 10 Ph.D. thesis supervisions;

over 20 lectures at international conferences;

over 60 publications;

Up to 5 selected publications from the past 5 years:

1. On Krein-von Neumann and Friedrichs extensions, Acta Sci. Math. (Szeged) 69 (2003),

323-336., /with E. Sikolya/.

2. On products of unbounded operators, Acta Math. Hung. 100 (1-2)(2003), 105-129.,

/with J. Stochel/.

3. Sebestyén Moment Problem: the multidimensional case, Amer. Math. Soc. 132 (2004) 1029-1035. (with Dan Popovici)

4. Reflection Symmetry and Symmetrizability of Hilbert space operators, Amer. Math. Soc. 133 (2005) 1727-1731 (with J. Stochel)

5. On the nonnegativity of operator products, Acta Math. Hung. 109(2005), 1-14. (with S. Hassi, H. de Snoo)

The five most important publications:

Every C*-seminorm is automatically submultiplicative Per. Math. Hung. 10 (1979), 1-8.

On the definition of C*-algebras II., Can. J. Math. 37 (1985), 664-681.

Restrictions of positive selfadjoint operators, Acta Sci. Math. (Szeged) 55 (1991), 149-154.

Operator extensions on Hilbert space, Acta Sci. Math. (Szeged) 57 (1993), 233-248.

Anticommutant lifting and anticommutant dilation, PAMS 121 (1995), 133-136.

Activity in the scientific community, international relations

Member of the Bolyai Math. Soc., Amer. Math. Soc.

Co-president of seven international conferences

Name: István Sigray

Date of birth: 1964

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant

Scientific degree (discipline):

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1988– ):

Analysis, and complex analysis (for students in mathematics; lecture, practice)

Riemann surfaces and Special functions (for students in mathematics; lecture)

Applyed complex analysis (for students in physics)

BSM (1995)

chapters from complex analysis (lecture, practice)

Other professional activity:

20 years of teaching experience, 4 diploma thesis supervisions, 2 lectures at international conferences;

2 publications;

Up to 5 selected publications from the past 5 years:

1. Solution of the polynomial equation kp’q–lpq’ = cp^m, Stud. Sci. Math. Hung. 45 (2008), 161–195..

The five most important publications:

1. On the monodromy representation of polynomial maps in n variables, Stud. Sci. Math. Hung. 39 (2002), 361–367.

2. Solution of the polynomial equation kp’q–lpq’ = cp^m, Stud. Sci. Math. Hung. 45 (2008), 161–195..

Activity in the scientific community, international relations

Name: Eszter Sikolya

Date of birth: 1976

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, assistant

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Magyary Zoltán Postdoctoral Scholarship (2006–2007)

Teaching activity (with list of courses taught so far):

Eötvös Loránd University (1998-2002, 2005– ):

analysis (for students in mathematics; lecture, practice)

partial differential equations (for students in physics; practice)

infinite dimensional dynamical systems (for students in mathematics; lecture)

University of Tübingen (2002-2004):

Functionalanalysis (for students in mathematics, parctice)

Other professional activity:

10 years of teaching experience, 1 diploma thesis supervisions;

10 lectures at international conferences;

9 publications;

3 international patents

Up to 5 selected publications from the past 5 years:

K.-J. Engel, M. Kramar Fijavž, R. Nagel, E. Sikolya, Vertex control of flows in networks. Networks and Heterogeneous Media, to appear.

E. Sikolya, A functional analytic method for the analysis of general partial differential equations. Probl. Program. 2006, no. 2-3, 669–673.

T. Mátrai and E. Sikolya, Asymptotic behavior of flows in networks. Forum Math. 19 (2007), 429–461.

M. Kramar and E. Sikolya, Spectral properties and asymptotic peridocity of flows in networks. Math. Z. 249 (2005), 139–162.

E. Sikolya, Simultaneous observability of networks of strings and beams. Bol. Soc. Paran. Mat. 21 Nr. 1/2 (2003), 1–11.

The five most important publications:

K.-J. Engel, M. Kramar Fijavž, R. Nagel, E. Sikolya, Vertex control of flows in networks. Networks and Heterogeneous Media, to appear.

M. Kramar, D. Mugnolo and E. Sikolya, Variational and semigroup methods for waves and diffusion in networks. Appl. Math. Optim. 55 (2007), 219–240.

T. Mátrai and E. Sikolya, Asymptotic behavior of flows in networks. Forum Math. 19 (2007), 429–461.

M. Kramar and E. Sikolya, Spectral properties and asymptotic peridocity of flows in networks. Math. Z. 249 (2005), 139–162.

E. Sikolya, Simultaneous observability of networks of strings and beams. Bol. Soc. Paran. Mat. 21 Nr. 1/2 (2003), 1–11.

Activity in the scientific community, international relations

Strasbourg, Prof. Komornik Vilmos (see the paper Simultaneous observability of networks of strings and beams)

Tübingen, Prof. Rainer Nagel (see the paper Spectral properties and asymptotic peridocity of flows in networks)

Rome, Prof. Klaus-Jochen Engel

Name: László Simon

Date of birth: 1940.

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, full professor

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far):

Eötvös University (1963– ):

Partial differential equations (for students in mathematics; lecture, practice)

analysis (for students in physics)

Other professional activity:

45 years of teaching experience, 8 diploma thesis supervisions, 7 Ph.D. thesis supervisions;

over 30 lectures at international conferences;

65 publications;

Up to 5 selected publications from the past 5 years:

1. W. Jäger, L. Simon: On nonlinear perturbations of the Schrödinger equation with discontinuous coefficients, Acta Math. Hung. 98 (2003), 227-243.

2. L. Simon: On approximation of solutions of parabolic functional differential equations in unbounded domains, Proceedings of the Conference FSDONA Teistungen, 2001, 439-451.

3. L. Simon: On nonlinear parabolic functional differential equations with nonlocal linear contact conditions, Funct. Diff. Equations 11(2004), 153-162.

4. On contact problems for nonlinear parabolic functional differential equations, Electronic J. of Qualitative Theory of Diff. Equations, 2004, 22, 1-11.

5. L. Simon, W. Jäger, On a system of quasilinear parabolic functional differential equations, Acta Math. Hung. 112 (2006), 39-55.

The five most important publications:

1. L. Simon: On approximation of solutions of boundary value problems in domains with unbounded boundary, Mat. Sbornik 91 (1973), 488-493.

2. L. Simon: On strongly nonlinear elliptic equations in unbounded domains, Differ. Uravneniya 22 (1986), 472-483.

3. L. Simon: Radiation conditions and the principle of limiting absorption for quasilinear elliptic equations, DAN SSSR 288 (1986), 316-319.

4. L. Simon: On strongly nonlinear elliptic equations with weak coercivity condition. Publ. Math. Barcelona 36 (1992), 175-188.

5. L. Simon: On nonlinear hyperbolic functional differential equations, Math. Nachr. 217 (2000), 175-186.

Activity in the scientific community, international relations

organizer of five international conferences;

member of the Mathematical Commitee of the Hungarian Academy of Sciences;

member of the granting committee of the Hungarian NSRF (OTKA), 1999–2003;

coauthor from Germany;

visiting professor at universities in Germany, Spain, Finland and Belgium.

Name: Péter Simon

Date of birth: 1966

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Loránd University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Bolyai scholarship (2000–2001 and 2003-2005)

Teaching activity (with list of courses taught so far):

Eötvös Loránd University (1990– ):

Differential equations (for students in mathematics and applied mathematics; lecture, practice)

Dynamical systems (for students in mathematics and applied mathematics; lecture, practice)

Mathematical modelling (for students in applied mathematics; practice)

Analysis (for students in physics; lecture, practice)

Analysis (for students in mathematics and applied mathematics; practice)

Calculus (for students in physics; lecture, practice)

BSM (2003– )

Dynamical systems

Real functions and measures

Other professional activity:

18 years of teaching experience, 6 diploma thesis supervisions, 2 Ph.D. thesis supervisions;

over 25 lectures at international conferences;

53 publications;

International collaborations (Leeds, Vienna)

Up to 5 selected publications from the past 5 years:

1. J. Karátson, P.L. Simon, Exact multiplicity for degenerate two-point boundary value problems with p-convex nonlinearity, , J. Nonlin. Anal., 52 (6), 1569-1590 (2003).

2. P. L. Simon, On the structure of of spectra of travelling waves, E. J. Qualitative Theory of Diff. Equ., 15, 1-19, (2003).

3. Tóth, J., Simon P.L., Differenciálegyenletek; Bevezetés az elméletbe és az alkalmazásokba, Typotex, (2005).

4. Simon, P.L., Classification of positive convex functions according to focal equivalence, IMA J. Appl. Math., 71, 519-533 (2006).

5. Simon, P.L., Volford, A., Detailed study of limit cycles and global bifurcations in a circadian rhythm model, Int. J. Bif. Chaos,16 (2), 349-367 (2006).

The five most important publications:

B.M. Garay, P.L. Simon, The local flow-box theorem for discretizations. The analytic case, J. Difference Eqns. Appl., 7, 345-381, (2001).

J. Karátson, P.L. Simon, On the linearized stability stability of positive solutions of quasilinear problems with p-convex or p-concave nonlinearity, J. Nonlin. Anal., 47, 4513-4520, (2001).

J. Hofbauer, P.L. Simon, An existence theorem for parabolic equations on ${\bf R}^N$ with discontinuous nonlinearity, E. J. Qualitative Theory of Diff. Equ., No. 8., 1-9 (2001).

Simon, P.L., Kalliadasis, S., Merkin, J.H., Scott, S.K., Stability of flames in an exothermic-endothermic system, IMA J. Appl. Math., 69, 175-203, (2004).

J. Hernandez, J. Karátson, P.L. Simon, Multiplicity for semilinear elliptic equations involving singular nonlinearity, J. Nonlin. Anal., 65 (2), 265-283 (2006).

Activity in the scientific community, international relations

Collaboration with J. Hofbauer (Vienna) 1997-2001.

Bolyai János Fellowship: 2000-2001, 2003-2005.

Research Fellowship at the University of Leeds: 2001-2002.

OTKA (Hungarian Science Foundation) grant: 1997-2000, 2001-2004.

Name: András Stipsicz

Date of birth: 1966

Highest degree: diploma in mathematics,

Present employer: Alfréd Rényi Mathematical Institute, scientific advisor

Scientific degree: DSc (mathematics)

Major Hungarian Scholarship: Széchenyi István Scholarship: 2001

Bolyai János Scholarship, 1999-2002

Teaching activity (with list of courses taught so far):

Eötvös University (1997-2002):

Analysis, algebraic topology, differential topology

BSM (Budapest Semester in Mathematics) 1997-

analysis, toplogy

Other professional activity:

Research in mathematics since 1990

Over 10 years of teaching

Up to 5 selected publications from the past 5 years:

Ozsváth-Szabó invariants and tight contact 3-manifolds I (Paolo Lisca-val közösen) Geom. Topol. 8 (2004) 925-945.

An exotic smooth structure on CP2#6CP2-bar (Szabó Zoltánnal közösen) Geom. Topol. 9 (2005) 813-832

Ont he geography of Stein fillings of certain 3-manifolds, Michigan Math. J. 51 (2003) 327-337

Seifert fibered contact 3-manifolds via surgery (Paolo Lisca-val közösen) Algebr. Geom. Topol. 4 (2004) 199-217.

Tight, non-fillable contact circle bundles (Paolo Lisca-val közösen) Math. Ann. 328 (2004) 285-298.

The five most important publications:

Ozsváth-Szabó invariants and tight contact 3-manifolds I (Paolo Lisca-val közösen)Geom. Topol. 8 (2004) 925-945.

4-manifolds and Kirby calculus (Robert Gompf-fal közösen)

AMS Graduate Studies in Math. Vol. 20 (1999)

Seifert fibered contact 3-manifolds via surgery (Paolo Lisca-val közösen)

Algebr. Geom. Topol. 4 (2004) 199-217.

Tight, non-fillable contact circle bundles (Paolo Lisca-val közösen)

Math. Ann. 328 (2004) 285-298.

Activity in the scientific community, international relations

Guest professor/reseracher at several universities ( (UC Irvine, MSRI Berkeley, Princeton University, IAS Princeton, Warwick University, Max-Planck-Institute Bonn, Columbia University),

Invited address at several conferences

Organizer of several conferences and summer schools

Name: Csaba Szabó

Date of birth: 1965

Highest degree: diploma in mathematics,

Present employer: Associate Professor, ELTE, Dept of Algebra and Number Theory

Scientific degree: DSc (mathematics)

Major Hungarian Scholarship: Széchenyi István Scholarship: 2001

Bolyai János Scholarship, 1998-2001

Teaching activity:

Eötvös University (1986– )

algebra, algebra and number theory, linear algebra

Abroad:

calculus I-II., linear algebra

Budapest Semesters in Mathematics (1998– )

algebra, Galois theory, number Theory

Other professional activity:

3x1 years Post Doctoral Fellowship

Up to 5 selected publications from the past 5 years:

1. Pluhár Gabriella; Szabó Csaba The free spectrum of the varieties of bands, Semigroup Forum, Vol. 76, (2008) No. 3. 576-578

2. Kátai-Urbán, Kamilla; Szabó, Csaba On the free spectrum of the variety generated by the combinatorial completely 0-simple semigroups. Glasg. Math. J. 49 (2007), no. 1, 93–98.

3. Horváth, Gábor; Lawrence, John; Mérai, László; Szabó, Csaba The complexity of the equivalence problem for nonsolvable groups. Bull. Lond. Math. Soc. 39 (2007), no. 3, 433–438.

4. Kátai-Urbán, Kamilla; Szabó, Csaba Free spectrum of the variety generated by the five element combinatorial Brandt semigroup. Semigroup Forum 73 (2006),

5. Szabó, Csaba On rings with few orbits. Comm. Algebra 34 (2006), no. 6, 2251–2260.

The five most important publications:

1. Cs. Szabó és P. J. Cameron, Independence algebras, J. London Math.Soc. (2) 61 (2000) 321–334.

2. Cs. Szabó és R. W. Quackenbush, Nilpotent groups are not dualizable, Journal of Australian Mathematical Society, 73 (2002) 173–179.

3. Cs. Szabó és R. W. Quackenbush, Strong duality for metacyclic groups, Journal of Australian Mathematical Society 72 (2002) 377–392.

4. Cs. Szabó et al., Natural dualities for quasi-varieties generated by a finite commutative ring, The Victor Aleksandrovich Gorbunov memorial issue Algebra Universalis, 46 (2001), 285–320.

5. Cs. Szabó, Nilpotent rings are not dualizable, Algebra Universalis, 42 (1999) 293–298.

Name: István Szabó

Date of birth: 1948

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Loránd University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian Scholarships:

Teaching activity (with list of courses taught so far):

Eötvös Loránd University (1991– ):

Applied information theory and algebra (for students in mathematics, for student for informatics; lecture, practice):

Data Compression, Cryptography

Other professional activity:

20 years of teaching experience;

20 publications;

1 technical book revision

1 Hungarian patent;

Expert titles: Electronic signature service expert

Up to 5 selected publications from the past 5 years:

- I. Szabó: System of courses and tools in the field of technological security evaluation methodology, HISEC’2004 (Hungarian Information Security Conference), 2004.

-. I. Szabó: Common Criteria – Educational curriculum, Published by Ministry of Informatics and Telecommunication, 2004

-. I. Szabó: IT security and covert channels, SAP’2006 Conference, 2006

-. P.Papp, I. Szabó: Different approaches to the security of cryptography- based security mechanisms, Journal of Applied Mathematics, 23 (2006) .207-294

The five most important publications:

“On matrix characterizations of primitive regular semigroups”, Coll. Math.Soc.,39, 461-469

“On a class of lattice ordered semigroups”, Acta Math. Ac.Sci. Hung.,30,141-147

“Laws, Organisations, Recommendations and Practice”, Global IT Security, Österreichische Computer Gesellschaft, Proceedings of the XV. IFIP World Computer Congress, 1998

Book-like publications (in many copies, published on Internet by governmental organisation) determining educational and professional orientation, revised by wide audience:

„Common Criteria Methodology for security evaluation of IT products and systems”, Recommendation document No 16 by MEH ITB, www.itb.hu/ajanlasok/a16 , 1998., Published by the Interministerial Committee on Informatics of the Prime Minister’s Office

„IT Security Sectorial Strategy of Hungarian Information Society Strategy ”, Published by Ministry of Informatics and Telecommunication, 2004

STUDY on the possible tasks of the National Communications Authority regarding the IT Security Sectorial Strategy of Hungarian Information Society Strategy, 2004

Activity in the scientific community, international relations

Member of the following professional associations: John von Neumann Computer Society, Hungarian Electronic Signature Association.

Presentations, participation at different conferences.

Name: Mihály Szalay.

Date of birth: 1947

Highest degree (discipline): M.Ed. in Mathematics and Physics

Present employer: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Teaching activity (with list of courses taught so far):

Eötvös University (1970– ):

algebra and number theory (for students in mathematic and physics; practice)

linear algebra and geometry (for students in informatics; lecture, practice)

number theory (for student in mathematics; lecture, practice)

group theory (for students in physics; lecture)

analytic number theory (for students in mathematics; lecture)

power sum method and its applications; statistical theory of partitions; statistical theory of groups; chapters from number theory (special courses (lectures) for students in mathematics).

Other professional activity:

37 years of teaching experience.

24 research papers, 2 survey papers, 1 textbook.

Up to 5 selected publications from the past 5 years:

1. Nicolas, J.-L., Szalay, M.: Popularity of sets represented by the partitions of n, The Ramanujan Journal 8 (2004), 147–175.

2. Dartyge, C., Sárközy, A., Szalay, M.: On the distribution of the summands of partitions in residue classes, Acta Math. Hunmgar. 109 (2005), 215–237.

3. Dartyge, C., Sárközy, A., Szalay, M.: On the number of prime factors of summands of partitions, Journal de Théorie des Nombres de Bordeaux 18 (2006), 73–87.

4. Dartyge, C., Sárközy, A., Szalay, M.: On the distribution of the summands of unequal partitions in residues classes, Acta Math. Hungar. 110 (2006), 323–335.

5. Dartyge, C., Szalay, M.: Dominant residue classes concerning the summands of partitions, Functiones et Approximatio 37 (2007), 65–96.

The five most important publications:

1. Szalay, M., Turán, P.: On some problems of the statistical theory of partitions with application to characters of the symmetric group, I, Acta Math. Acad. Sci. Hungar. 29 (1977), 361–379.

2. Erdős, P., Szalay, M.: On some problems of J. Dénes and P. Turán, in: Studies in Pure Mathematics (to the Memory of Paul Turán), Akadémiai Kiadó, Budapest, 1983, 187–212.

3. Erdős, P, Szalay, M.: On the statistical theory of partitions, in: Coll. Math. Soc. J. Bolyai, 34 (Topics in Classical Number Theory, Budapest, 1981), 397–450.

4. Erdős, P, Nicolas, J.-L., Szalay, M.: Partitions into parts which are unequal and large, in: Lecture Notes in Mathematics 1380 (Number Theory, Ulm, 1987), Springer, Berlin–Heidelberg–New York, 1989, 19–30.

5. Dartyge, C., Szalay, M.: Dominant residue classes concerning the summands of partitions, Functiones et Approximation 37 (2007), 65–96.

Activity in the scientific community, international relations

Matematikai Lapok (technical editor), 1985–1990;

Network ERBCI PACT 92-4022 (ELTE–coordinator), 1992–1995;

Mathematical Reviews (reviewer), 1987–;

Zentralblatt für Mathematik (reviewer), 1987–;

coauthors from France, U.K., U.S.A.;

invited professor at the University Henri Poincaré, Nancy 1.

Name: Péter Sziklai

Date of birth: 1968

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Major Hungarian scholarships: Bolyai scholarship, Eötvös scholarship, Magyary postdoctoral fellowship, OTKA postdoctoral grant

Teaching activity (with list of courses taught so far):

Discrete mathematics, practice/lecture (for students in teaching of math., mathematics, applied math.): since 1989 (15 years, 3-4 years missed)

Geometry practice (for students in teaching of math.): 1989-91 (2 years)

Set theory and logic practice (for students in teaching of math.): 4 years

Finite geometry seminar: 10 years approx.

Introduction to finite geometry, lecture: 4 years

Symmetric structures, lecture (students in mathematics): 2 év

Graphs and algorithms lecture (for students in teaching of math.): 3 years

Introduction to computer science, lecture, practice (BTU, stutents in informatics): 5 years

Elements of computer science, lecture (BTU ): 2 years

Calculus (CEU, Environmental studies): 3 years

Other professional activity:

19 years of teaching experience, 7 diploma thesis supervisions, 1 Ph.D. thesis supervisions;

over 20 lectures at international conferences;

25 publications;

2 patents pending

Up to 5 selected publications from the past 5 years:

1. J. Eisfeld, L. Storme and P. Sziklai, On the spectrum of the sizes of maximal partial spreads in PG(2n,q), q>=3, Des. Codes Cryptogr., 36 (2005), 101-110.

2. P. Sziklai, Partial flocks of the quadratic cone, J. Combin. Th. Ser. A, 113 (2006), 698-702.

3. P. L. Erdős, P. Ligeti, P. Sziklai, D. Torney, Subwords in reverse complement order, Annals of Comb., 10 (2006), 415-430.

4. S. Ball, A. Blokhuis, A. Gács, P. Sziklai and Zs. Weiner, On linear codes whose weights and length have a common divisor, Advances in Mathematics 211 (2007), 94-104.

5. P. Sziklai, A conjecture and a bound on the number of points of a plane curve, Finite Fieds Appl., 14 (2008), 41-43.

The five most important publications:

1. J. Eisfeld, L. Storme and P. Sziklai, On the spectrum of the sizes of maximal partial spreads in PG(2n,q), q>=3, Des. Codes Cryptogr., 36 (2005), 101-110.

2. P. Sziklai, Partial flocks of the quadratic cone, J. Combin. Th. Ser. A, 113 (2006), 698-702.

3. P. L. Erdős, P. Ligeti, P. Sziklai, D. Torney, Subwords in reverse complement order, Annals of Comb., 10 (2006), 415-430.

4. S. Ball, A. Blokhuis, A. Gács, P. Sziklai and Zs. Weiner, On linear codes whose weights and length have a common divisor, Advances in Mathematics 211 (2007), 94-104.

5. P. Sziklai, A conjecture and a bound on the number of points of a plane curve, Finite Fieds Appl., 14 (2008), 41-43.

Activity in the scientific community, international relations

Combinatorica (Springer-Bolyai), Managing Editor

organizer of two international conferences;

member of Hungarian-Spanish/Flemish/Italian/Slovenian/Dutch bilateral projects in past

member of the granting committee of the Rényi Kató Prize;

head of ELTECRYPT research group

Name: Róbert Szőke

Date of birth: 1958

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics), Ph.D(mathematics)

Major Hungarian scholarships: Széchenyi professor scholarship (2000–2003)

Teaching activity (with list of courses taught so far):

Notre Dame University (1985-1990)

Calculus, (for undergraduate students, practice)

Ordinary Differential equations (for undegraduate students, practice),

Since January 1, 1991 I teach at the Department of Analysis at Eötvös University, except certain short periods, see below.

Eötvös University (1991– ):

analysis (for students in mathematics; mathematics- physics or technology education; informatics-physics; astronomy; geophysics; lecture, practice)

complex analysis (for tudents in mathematics;mathematics or physics education;astronomy; lecture, practice)

several complex variables (for tudents in mathematics; lecture)

complex manifolds (for PhD students, lecture)

BSM (2004 Spring semester)

Basic Algebraic geometry (lecture)

CEU (2004 Fall semester)

Complex manifolds (Reading course)

Purdue University

Linear algebra and ordinary differential equations (1997 Spring semester, for students in engineering, lecture)

Ordinary differential equations (2005 Spring semester, for students in engineering, lecture)

Linear algebra (2007 Fall semester, for students in engineering, lecture)

Other professional activity:

Sept 1977- June 1978: computer operator in the Computer center of the Ministry of Labour

Nov. 1983- Aug. 1984 and Aug.-Dec. 1990: scientific coworker, Computer center of the Medical University

Sept. 1984- Aug. 1985: guest researcher at the Mathematical Institute of the Hungarian Academy of Sciences,

Aug. 1985- Aug. 1990: graduate student at the University of Notre Dame

October 1992- Aug. 1994: guest researcher at the Max Planck Institut für Mathematik, Bonn

Sept. -Dec. 1999: guest researcher (with an Eötvös fellowship) at the Mathematical Institute of Oxford University

Feb.- Dec. 2008: guest researcher at the Rényi Institute of Mathematics

Up to 5 selected publications from the past 5 years:

1. R. Szőke: Canonical complex structures associated to connections and complexifications of Lie groups (Math. Ann. 329, 553-591, 2004)

2. R. Szőke: Többváltozós komplex függvénytan (egyetemi jegyzet, 2003, ELTE, Eötvös kiadó)

3. R. Szőke: Complex crowns of symmetric spaces (Int. J. Math. 16, 889-902, 2005)

4. A. Korányi, R. Szőke: On Weyl group equivariant maps (Proc. AMS, 134, 3449-3456, 2006)

5. R. Szőke: On isometries of Kahler manifolds (Acta Math. Hung. 111, 77-79, 2006)

The five most important publications:

1. L. Lempert-R. Szőke: Global solutions of the homogeneous Monge-Ampere equation and complex structures on the tangent bundles of Riemannian manifolds (Math. Ann. 290, 689-712, 1991)

2. R. Szőke: Complex structures on the tangent bundle of Riemannian manifolds (Math. Ann. 291, 409-428, 1991)

3. A. Dancer- R. Szőke: Symmetric spaces, adapted complex structures and hyperkahler structures (Q. J. Math., 48, 27-38, 1997)

4. R. Szőke: Involutive structures on the tangent bundle of symmetric spaces (Math. Ann.,

319, 319-348, 2001)

5. R. Szőke: Canonical complex structures associated to connections and complexifications of Lie groups (Math. Ann. 329, 553-591, 2004)

Activity in the scientific community, international relations

Member of the Bolyai Mathematical Society and the AMS.

Referee of NSF and OTKA proposals and international math journals.

Name: Tamás Szőnyi

Date of birth: 1957

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, professor, Computer and Automation Research Institute, Hungarian Academy of Sciences, research advisor (part time)

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1997–2000), Pál Erdős Prize of the Hungarian Academy (1997).

Teaching activity (with list of courses taught so far):

Eötvös University (1987– ):

Discrete mathematics (for students in mathematics; lecture, practice; also for students in

informatics)

Symmetric structures, finite geometry, Mathematical games, Extremal set systems, Enumeration, Error correcting codes,

Finite geometry seminar (research seminar 1986--)

University of Szeged (1994--1997)

Geometries and their models, Algebraic methods in combinatorics, Plane curves, Codes and geometries (for students in mathematics)

Technical University Budapest (1982--1993)

Mathematics I,II,III, IV (for students in transportation engineering)

Other professional activity:

25 years of teaching experience, 15 diploma thesis supervisions, 7 Ph.D. thesis supervisions; over 30 lectures at international conferences; 1 book in Hungarian,

65 publications

Visiting professor Yale, TUE Eindhoven, University of Sussex, University of Ghent, University of Perugia, University of Basilicata (in total roughly 26 months)

Up to 5 selected publications from the past 5 years:

A. Gács, T. Szőnyi , Zs. Weiner, On the spectrum of minimal blocking sets, J. of Geometry, 76 (2003), 256-281

A. Gács , T. Szőnyi, On maximal partial spreads on PG(n,q), Designs, Codes, and

Cryptography 29 (2003), 123-129

E. Boros, T. Szőnyi, K. Tichler. Defining sets for PG(2,q), Discrete Mathematics 30

(2005), 17—31.

J. Barát, F. Pambianco, S. Marcugini, T. Szőnyi, On disjoint blocking sets, J.

Comb. Designs 14 (2006), 149—158.

A. Blokhuis, L. Lovász, L. Storme, T. Szőnyi, On multiple blocking sets in Galois planes,

Advances in Geometry 7 (2007), 39—53.

The five most important publications:

E. Boros, T. Szőnyi, On the sharpness of a theorem of B. Segre, Combinatorica 6 (1986), 261-268

L. Rónyai, T. Szőnyi, Planar functions over finite fields, Combinatorica 9 (1989), 315-320

T. Szőnyi, Blocking sets in Desarguesian affine and projective planes, Finite Fields and Appl. 2 (1997), 187-202

T. Szőnyi, On the embedding of (k,p)-arcs in maximal arcs, Designs, Codes, and Cryptography 18 (1999), 235-246

A. Blokhuis, L. Storme, T. Szőnyi, Multiple blocking sets in Desarguesian planes,

J. London Math. Soc.60 (1999), 321-332

Activity in the scientific community, international relations

member of the J. Bolyai Math. Society, reviewer of Mathematical Reviews,

secretary and later vice president of the Mathematical Committee of the Hungarian

Academy of Sciences (1999--), member of the OTKA Jury in mathematics

(1998—2001),

Editor of Combinatorica, Innovations in Incidence Geometry, Abh. Math. Sem.

Univ. Hamburg, Contributions to Discrete Mathematics, Annales Univ. Eötvös,

Sect Math.

Organizer of 4 international conferences, editor of 3 conference proceedings

International relations: TUE Eindhoven, Universities of Ghent, Perugia, Potenza,

Sussex.

Name: András Szűcs

Date of birth: 1950

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, full professor

Scientific degree (discipline): DSc (mathematics)

Major Hungarian scholarships: Széchenyi scholarship (1997—2000)

Teaching activity (with list of courses taught so far):

Eötvös University (1981– ):

geometry, analysis, complex analysis, topology

BSM (1988)

Algebraic topology

Other professional activity:

30 years of teaching experience, many diploma thesis supervisions, 2 Ph.D. thesis supervisions;

over 10 invited (1 hour) lectures at international conferences;

51 publications;

Up to 5 selected publications from the past 5 years:

1) with T. Ekholm: Geometric formulas for Smale invariants of codimension two immersions, Topology 42 (2003) 171 – 196

2) with G. Lippner: A new proof of the Herbert multiple-point formula (Russian) Fundam. Prikl. Mat. 11 (2005) no 5, 107 – 116; translation in J. Math. Sci (N.Y.) 146 (2007), no 11, 5523 – 5529.

3) Elimination of Singularities by Cobordism, Real and complex singularities, 301 – 324, Contemporary Mathematics Volume 354, Amer Math. Soc., Providence, RI, 2004

4) with T. Ekholm and T. Terpai: Cobordism of fold maps and maps with prescribed number of cusps. Kyushu J. Math. 61 (2007), no 2, 395 – 414.

5) Cobordism of singular maps, Geometry and Topology 12 (2008) 2379-2452.

The five most important publications:

1) Analogue of the Thom space for mapping with singularity of type Sigma1, Math. Sb. (N. S.) 108 (150) (1979) no. 3 438 – 456 (in Russian); English translation: Math. USSR-Sb. 36 (1979) no. 3. 405 – 426 (1980)

2) Cobordism group of immersions of oriented manifolds; Acta Math. Hungar. 64 (2) (1994), 191 – 230

3) with R. Rimanyi: Pontrjagin – Thom type construction for maps with singularities, Topology 37 (1998), 1177 – 1191

4) with T. Ekholm: Geometric formulas for Smale invariants of codimension two immersions, Topology 42 (2003) 171 – 196

5) Cobordism of singular maps, Geometry and Topology 12 (2008) 2379 – 2452.

Activity in the scientific community, international relations:

Secretary of the Doctoral Committee of the Hungarian Academy of Siences (5 years)

Secretary of the Hungarian Topology Conference (20 years)

Member of the doctoral committee on a large number of occasions

Editor of Mathematica Slovaca.

Name: Árpád Tóth

Date of birth: 1964

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: Bolyai Fellowship

Teaching activity (with a selection of courses taught so far):

Eötvös University (2003– ):

Analysis (for students in math, math ed; lecture, practice)

Calculus (for students in physics education; lecture, practice)

Ordinary Differential Equations (for students in physics edutacttion; lecture, practice)

Modular Forms (for students in math, lecture)

Several Complex Variables (for students in math, lecture)

Topology (for students in math, lecture)

BSM (2004– )

Topology (lecture, practice)

Analytic Number Theory (lecture, practice)

Fordham University (2001-2003)

Calculus (for students in math, business, life sciences; lecture, practice)

Linear Algebra (for students in math; lecture, practice)

Finte Math with Probability (for liberal arts students; lecture, practice)

University of Michigan (1997-2000)

Calculus ((various versions) for students in math, engineering, business, life sciences; lecture, practice)

Linear Algebra (for students in engineering; lecture, practice)

Ordinary Differential Equations (for students in engineering; lecture, practice, computer lab)

Advanced Vector Calculus (for graduate students in engineering; lecture, practice)

Number Theory (for students in math; lecture, practice)

Modular Forms (for PhD students in math, lecture)

Rutgers University (1992-1997)

Calculus (for students in math, engineering, business, life sciences; lecture, practice)

Vector Calculus (for students in physics, engineering; lecture, practice)

Ordinary Differential Equations (for students in engineering; practice)

Advanced Vector Calculus (for master students in applied math; practice)

Other professional activity:

More than 15 years of teaching experience, over 15 lectures at international conferences;

8 publications;

Up to 5 selected publications from the past 5 years:

1. Toth A., Varolin D. Holomorphic diffeomorphisms of semisimple homogeneous spaces. Compos. Math. 142 (2006), no. 5, 1308—1326.

2. Elekes M., Toth A. Covering locally compact groups by less than $2\sp \omega$ many translates of a compact nullset. Fund. Math. 193 (2007), no. 3, 243--257.

3. Toth A. On the Steinberg module of Chevalley groups. Manuscripta Math. 116 (2005), no. 3, 277--295.

4. Toth A., On the evaluation of Salié sums. Proc. Amer. Math. Soc. 133 (2005), no. 3, 643--645

5. Duke W., Toth A. The splitting of primes in division fields of elliptic curves. Experiment. Math. 11 (2002), 555--565

The five most important publications:

1. Toth A., Varolin D. Holomorphic diffeomorphisms of semisimple homogeneous spaces. Compos. Math. 142 (2006), no. 5, 1308—1326.

2. Toth A., Roots of quadratic congruences. Internat. Math. Res. Notices 2000, no. 14, 719--739.

3. Toth A. On the Steinberg module of Chevalley groups. Manuscripta Math. 116 (2005), no. 3, 277--295.

4. Toth A., On the evaluation of Salié sums. Proc. Amer. Math. Soc. 133 (2005), no. 3, 643--645

5. Duke W., Toth A. The splitting of primes in division fields of elliptic curves. Experiment. Math. 11 (2002), no. 4, 555--565

Name: László Verhóczki

Date of birth: 1961

Highest degree (discipline): diploma in mathematics and physics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): PhD (mathematics)

Major Hungarian scholarships: –

Teaching activity (with list of courses taught so far):

Technical University of Budapest (1985–1997):

Geometry (all levels, lecture, practice)

Descriptive Geometry (lecture, practice)

Differential Geometry (lecture, practice)

Calculus (practice)

Eötvös University (1997– )

Geometry (all levels, lecture, practice)

Differential Geometry (all levels, lecture, practice)

Other professional activity:

23 years of teaching experience, 11 diploma thesis supervisions;

over 13 lectures at international conferences;

15 publications.

Up to 5 selected publications from the past 5 years:

1. Verhóczki, L.: Special cohomogeneity one isometric actions on irreducible symmetric

spaces of types I and II, Beiträge Algebra Geom. 44 (2003), 57–74.

2. Csikós, B., Verhóczki, L.: Tubular structures of compact symmetric spaces associated

with the exceptional Lie group F₄, Geometriae Dedicata 109 (2004), 239–252.

3. Verhóczki, L.: The exceptional compact symmetric spaces G₂ and G₂/SO(4) as tubes,
Monatshefte für Mathematik 141 (2004), 323–335.

4. Csikós, B., Németh, B., Verhóczki, L.: Volumes of principal orbits of isotropy subgroups

in compact symmetric spaces, Houston J. Math. 33 (2007), 719–734.

5. Csikós, B., Verhóczki, L.: Classification of Frobenius Lie algebras of dimension ≤6,
Publicationes Math. Debrecen 70 (2007), 427–451.

The five most important publications:

1. Verhóczki, L.: Reflections of Riemannian manifolds, Publicationes Math. Debrecen
38 (1991), 19–31.

2. Verhóczki, L.: Special isoparametric orbits in Riemannian symmetric spaces,
Geometriae Dedicata 55 (1995), 305–317.

3. Verhóczki, L.: Shape operators of orbits of isotropy subgroups in Riemannian symmetric
spaces of the compact type, Beiträge Algebra Geom. 36 (1995), 155–170.

4. Berndt, J., Vanhecke, L., Verhóczki, L.: Harmonic and minimal unit vector fields on
Riemannian symmetric spaces, Illinois J. Math. 47 (2003), 1273–1286.

5. Csikós, B., Németh, B., Verhóczki, L.: Volumes of principal orbits of isotropy subgroups

in compact symmetric spaces, Houston J. Math. 33 (2007), 719–734.

Activity in the scientific community, international relations

organizer of three international conferences;

member of the Bolyai Mathematical Society (1988–);

coauthors from Belgium and Germany;

visiting professor at universities in Belgium and Germany.

Name: Katalin Vesztergombi

Date of birth: 1948

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös Lorand University, associate professor

Scientific degree (discipline): CSc (mathematics) 1987

Major Hungarian scholarships:

Teaching activity (with list of courses taught so far): Algorithmic geometry, discrete mathematics, discrete programing, combinatorial optimization, discrete mathematical models, calculus, differential equations, complex analysis, graphtheory, linear algebra, numerical methods, ALGOL; 32 years

Other professional activity:

Teaching and research: ELTE, JATE, BME, Rutgers University, Yale University, University of Washington, Microsoft Research (Redmond)

1 international patent

Up to 5 selected publications from the past 5 years:

Geometric representations of graphs (with L. Lovász), Paul Erdős and his Mathematics, (ed. G. Halász, L. Lovász, M. Simonovits, V.T. Sós), Bolyai Society--Springer Verlag (2004).

Quadrilaterals and k-sets (with L. Lovász, U. Wagner, E. Welzl) in: Towards a Theory of Geometric Graphs, (J. Pach, Ed.), AMS Contemporary Mathematics 342 (2004) 139-148.

Graph limits and parameter testing (with C.Borgs, J.Chayes, L.Lovász, V.T.Sós, B.Szegedy) STOC 2006

Counting graph homomorphisms (with C.Borgs, J.Chayes, L.Lovász, V.T.Sós) in: Topics in Discrete Mathematics (ed. M.Klazar, J.Kratochvil, M.Loebl, J.Matousek,R.Thomas, P.Valtr)

Springer (2006), 315-371

The five most important publications:

Activity in the scientific community, international relations

Name: András Zempléni

Date of birth: 1960

Highest degree (discipline): diploma in mathematics

Present employer, position: Eötvös University, associate professor

Scientific degree (discipline): CSc (mathematics)

Teaching activity (with list of courses taught so far):

Eötvös University (1982– ):

Probability theory (for students in applied mathematics, informatics, meteorology, geology; lecture, practice)

Mathematical statistics (for students in applied mathematics, informatics, meteorology, geology; lecture, practice)

Industrial statistics (for students in applied mathematics)

Modelling environmental data (for PhD students in mathematics)

Teaching experience: 25 years

Lecture note: Móri F. Tamás, Szeidl László, Zempléni András: Mathematical statistics exercises (Budapest, 1997, ELTE Eötvös Press)

Other professional activity:

25 years of teaching experience, 20 diploma thesis supervisions, 1 Ph.D. thesis supervision

Over 20 lectures at international conferences

52 publications

Coordinator of several major projects in applied statistics

Head of the Applied Statistical Consulting Group (1998-)

Teaching in German: KVIF, Statistics, 2002-

Participation in the English MSc courses held at Eötvös University, Department of Probability Theory and Statistics

Grants: Royal Society Postdoctoral Fellowship (Sheffield, 1991/92), Bolyai János research grant (1998-2000), DAAD grant (München, 2003)

Up to 5 selected publications from the past 5 years:

Taylor, C.C., Zempléni, A.: Chain Plot: a Tool for Exploiting Bivariate Temporal Structures Computational Statistics and Data Analysis, 2004, pp 141-153

Zempléni, A., Véber, M., Duarte, B. and Saraiva, P.: Control Charts: a cost-optimization approach for processes with random shifts. Appl. Stoch. Models in Business and Industry, 20, p.185-200, 2004 .

Dryden, I.L., Zempléni, A.: Extreme shape analysis. J. Roy. Stat. Soc., Ser. C, 55, part 1, p. 103-121. 2006.

Arató, N.M., Bozsó,D., Elek, P., Zempléni, A.: Forecasting and simulating mortality tables. Accepted, Mathematical and Computer Modelling, 2008.

Elek, P., Zempléni, A.: Tail behaviour and extremes of two-state Markov-switching autoregressive models. Computers and Mathematics, with applications, 55, p. 2839-2855, 2008.

The five most important publications:

Zempléni, A.: On the heredity of Hun and Hungarian property, J. of Theoretical Probability Vol 3. No.4. 1990, p. 599-609.

Zempléni, A.: Inference for bivariate extreme value distributions. Journal of Applied Statistical Science 1996, 4, No. 2/3, p. 107-122.

Taylor. C.C., Zempléni, A.: Chain Plot: a Tool for Exploiting Bivariate Temporal Structures. Computational Statistics and Data Analysis 46, p. 141-153, 2004

Dryden, I.L., Zempléni, A.: Extreme shape analysis. J. Roy. Stat. Soc., Ser. C, 55, part 1, p. 103-121. 2006.

Elek, P., Zempléni, A. Tail behaviour and extremes of two-state Markov-switching autoregressive models. Computers and Mathematics, with applications, 55, p. 2839-2855, 2008.

Activity in the scientific community, international relations:

Coordinator of several EU projects

Member of the European Regional Committee of the Bernoulli Society (2004-)

Coauthors from the United Kingdom, the Netherlands

Organisor of 3 conferences

MSc in Mathematics: Course descriptions

Title of the course: Algebraic and differential topology

Number of contact hours per week: 4+2

Credit value: 6+3

Course coordinator(s): András Szűcs

Department(s): Department of Analysis

Evaluation: oral examination + grade for problem solving

Prerequisites: Algebraic Topology course in BSC

A short description of the course:

Characteristic classes and their applications, computation of the cobordism ring of manifolds,

Existence of exotic spheres.

Textbook:

Further reading:

1) J. W. Milnor, J. D. Stasheff: Characteristic Classes, Princeton, 1974.

2) R. E. Stong: Notes on Cobordism Theory, Princeton, 1968.

Title of the course: Algebraic Topology (basic material)

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): András Szűcs

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: Algebraic Topology course in the BSC

A short description of the course:

Homology groups, cohomology ring, homotopy groups, fibrations, exact sequences, Lefschetz fixpoint theorem.

Textbook:

none

Further reading: R. M. Switzer: Algebraic Topology, Homotopy and Homology, Springer- Verlag, 1975.

Title of the course: Algorithms I

Number of contact hours per week: 2+2

Credit value: 2+3

Course coordinator(s): Zoltán Király

Department(s): Department of Computer Science

Evaluation: oral examination and tutorial mark

Prerequisites: none

A short description of the course:

Sorting and selection. Applications of dynamic programming (maximal interval-sum, knapsack, order of multiplication of matrices, optimal binary search tree, optimization problems in trees).

Graph algorithms: BFS, DFS, applications (shortest paths, 2-colorability, strongly connected orientation, 2-connected blocks, strongly connected components). Dijkstra’s algorithm and applications (widest path, safest path, PERT method, Jhonson’s algorithm). Applications of network flows. Stable matching. Algorithm of Hopcroft and Karp.

Concept of approximation algorithms, examples (Ibarra-Kim, metric TSP, Steiner tree, bin packing). Search trees. Amortization time. Fibonacci heap and its applications.

Data compression. Counting with large numbers, algorithm of Euclid, RSA. Fast Fourier transformation and its applications. Strassen’s method for matrix multiplication.

Textbook:

Further reading:

T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein: Introduction to Algorithms, McGraw-Hill, 2002

Title of the course: Analysis IV (for mathematicians)

Number of contact hours per week: 4+2

Credit value: 4+2

Course coordinator(s): János Kristóf

Department(s): Department of Applied Analysis and Computational Mathematics, Department of Analysis

Evaluation: oral or written examination, tutorial mark

Prerequisites:

A short description of the course:

Abstract measures and integrals. Measurable functions. Outer measures and the extensions of measures. Abstract measure spaces. Lebesgue- and Lebesgue-Stieltjes measure spaces. Charges and charges with bounded variation. Absolute continuous and singular measures. Radon-Nycodym derivatives. Lebesgue decomposition of measures. Density theorem of Lebesgue. Absolute continuous and singular real functions. Product of measure spaces. Theorem of Lebesgue-Fubini. L^p spaces. Convolution of functions.

Textbook: none

Further reading:

1) Bourbaki, N.: Elements of Mathematics, Integration I, Chapters 1-6, Springer-Verlag, New York-Heidelberg-Berlin, 2004.

2) Dieudonné, J.: Treatise On Analysis, Vol. II, Chapters XIII-XIV, Academic Press, New York-San Fransisco-London, 1976.

3) Halmos, Paul R.: Measure Theory, Springer-Verlag, New York-Heidelberg-Berlin, 1974.

4) Rudin, W.: Principles of Mathematical Analysis, McGraw-Hill Book Co., New York-San Fransisco-Toronto-London, 1964.

5) Dunford, N.- Schwartz, T.J.: Linear operators. Part I: General Theory, Interscience Publishers, 1958.

Title of the course: Analysis of time series

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): László Márkus

Department(s): Department of Probability Theory and Statistics

Evaluation: Oral examination

Prerequisites: Probability theory and Statistics,

Stationary processes

A short description of the course:

Basic notions of stationary processes,weak, k-order, strict stationarity, ergodicity, convergence to stationary distribution. Interdependence structure: autocovariance, autocorrelation, partial autocorrelation functions and their properties, dynamic copulas. Spectral representation of stationary processes by an orthogonal stochastic measure, the spectral density function, Herglotz’s theorem.

Introduction and basic properties of specific time series models: Linear models: AR(1), AR(2) AR(p), Yule-Walker equations, MA(q), ARMA(p,q), ARIMA(p,d,q) conditions for the existence of stationary solutions and invertibility, the spectral density function. Nonlinear models: ARCH(1), ARCH(p), GARCH(p,q), Bilinear(p,q,P,Q), SETAR, regime switching models. Stochastic recursion equations, stability, the Ljapunov-exponent and conditions for the existence of stationary solutions, Kesten-Vervaat-Goldie theorem on stationary solutions with regularly varying distributions. Conditions for the existence of stationary ARCH(1) process with finite or infinite variance, the regularity index of the solution.

Estimation of the mean. Properties of the sample mean, depending on the spectral measure. Estimation of the autocovariance function. Bias, variance and covariance of the estimator. Estimation of the discrete spectrum, the periodogram. Properties of periodogram values at Fourier frequencies. Expectation, variance, covariance and distribution of the periodogram at arbitrary frequencies. Linear processes, linear filter, impulse-response and transfer functions, spectral density and periodogram transformation by the linear filter. The periodogram as useless estimation of the spectral density function. Windowed periodogram as spectral density estimation. Window types. Bias and variance of the windowed estimation. Tayloring the windows. Prewhitening and CAT criterion.

Textbook: none

Further reading:

Priestley, M.B.: Spectral Analysis and Time Series, Academic Press 1981

Brockwell, P. J., Davis, R. A.: Time Series: Theory and Methods. Springer, N.Y. 1987

Tong, H. : Non-linear time series: a dynamical systems approach, Oxford University Press, 1991.

Hamilton, J. D.: Time series analysis, Princeton University Press, Princeton, N. J. 1994

Brockwell, P. J., Davis, R. A.: Introduction to time series and forecasting, Springer. 1996.

Pena, D., Tiao and Tsay, R.: A Course in Time Series Analysis, Wiley 2001.

Title of the course: Applications of Operations Research

Number of contact hours per week: 2+0

Credit value: 3+0

Course coordinator(s): Gergely Mádi-Nagy

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites: -

A short description of the course:

Applications in economics. Inventory and location problems. Modeling and solution of complex social problems. Transportation problems. Models of maintenance and production planning. Applications in defense and in water management.

Textbook: none

Further reading:

Title of the course: Approximation algorithms

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tibor Jordán

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

approximation algorithms for NP-hard problems, basic techniques,

LP-relaxations. Set cover, primal-dual algorithms. Vertex cover, TSP, Steiner tree, feedback vertex set, bin packing, facility location, scheduling problems, k-center, k-cut, multicut, multiway cut, multicommodity flows, minimum size k-connected subgraphs, minimum superstring, minimum max-degree spanning trees.

Textbook: V.V. Vazirani, Approximation algorithms, Springer, 2001.

Further reading:

Title of the course: Basic algebra (reading course)

Number of contact hours per week: 0+2

Credit value: 5

Course coordinator(s): Péter Pál Pálfy

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Basic group theory. Permutation groups. Lagrange’s Theorem. Homomorphisms and normal subgroups. Direct product, the Fundamental theorem of finite Abelian groups. Free groups and defining relations.

Basic ring theory. Ideals. Chain conditions. Integral domains, PID’s, euclidean domains.

Fields, field extensions. Algebraic and transcendental elements. Finite fields.

Linear algebra. The eigenvalues, the characterisitic polynmial and the minimal polynomial of a linear transformation. The Jordan normal form. Transformations of Euclidean spaces. Normal and unitary transformations. Quadratic forms, Sylvester’s theorem.

Textbook: none

Further reading:

I.N. Herstein: Abstract Algebra. Mc.Millan, 1990

P.M. Cohn: Classic Algebra. Wiley, 2000

I.M. Gel’fand: Lectures on linear algebra. Dover, 1989

Title of the course: Basic Geometry (reading course)

Number of contact hours per week: 0+2

Credit value: 5

Course coordinator(s): Gábor Moussong

Department(s): Department of Geometry

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Non-euclidean geometries: Classical non-euclidean geometries and their models. Projective spaces. Transformation groups.

Vector analysis: Differentiation, vector calculus in dimension 3. Classical integral theorems. Space curves, curvature and torsion.

Basic topology: The notion of topological and metric spaces. Sequences and convergence. Compactness and connectedness. Fundamental group.

Textbooks:

1. M. Berger: Geometry I–II (Translated from the French by M. Cole and S. Levy). Universitext, Springer-Verlag, Berlin, 1987.

2. P.C. Matthews: Vector Calculus (Springer Undergraduate Mathematics Series). Springer, Berlin, 2000.

3. W. Klingenberg: A Course in Differential Geometry (Graduate Texts in Mathematics). Springer-Verlag, 1978.

4. M. A. Armstrong: Basic Topology (Undergraduate Texts in Mathematics), Springer-Verlag, New York, 1983.

Further reading:

Title of the course: Business economics

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Róbert Fullér

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Monopoly, Lerner index; horizontal differentiation, the effect of advertisement and service; vertical differentiation; price discrimination; vertical control; Bertrand’s paradox, repeated games; price competition; tacit collusion; the role of R&D in the competition.

Textbook:

Jean Tirole, The Theory of Industrial Organization, The MIT Press, Cambridge, 1997.

Further reading:

Title of the course: Chapters of Complex Function Theory

Number of contact hours per week: 4+0

Credit value: 6

Course coordinator(s): Gábor Halász

Department(s): Department of Analysis

Evaluation: oral examination, home work and participation

Prerequisites: Complex Functions (BSc),

Analysis IV. (BSc)

A short description of the course:

The aim of the course is to give an introduction to various chapters of functions of a complex variable. Some of these will be further elaborated on, depending on the interest of the participants, in lectures, seminars and practices to be announced in the second semester. In general, six of the following, essentially self-contained topics can be discussed, each taking about a month, 2 hours a week.

Topics:

Phragmén-Lindelöf type theorems.

Capacity. Tchebycheff constant. Transfinite diameter. Green function. Capacity and Hausdorff measure. Conformal radius.

Area principle. Koebe’s distortion theorems. Estimation of the coefficients of univalent functions.

Area-length principle. Extremal length. Modulus of quadruples and rings. Quasiconformal maps. Extension to the boundary. Quasisymmetric functions. Quasiconformal curves.

Divergence and rotation free flows in the plane. Complex potencial. Flows around fixed bodies.

Laplace integral. Inversion formuli. Applications to Tauberian theorems, quasianalytic functions, Müntz’s theorem.

Poisson integral of L_p functions. Hardy spaces. Marcell Riesz’s theorem. Interpolation between L_p spaces. Theorem of the Riesz brothers.

Meromorphic functions in the plane. The two main theorems of the Nevanlinna theory.

Textbook:

Further reading:

M. Tsuji: Potential Theory in Modern Function Theory, Maruzen Co., Tokyo, 1959.

L.V. Ahlfors: Conformal Invariants, McGraw-Hill, New York, 1973.

Ch. Pommerenke: Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.

L.V. Ahlfors: Lectures on Quasiconformal Mappings, D. Van Nostrand Co., Princeton, 1966. W.K.Hayman: MeromorphicFunctions, Clarendon Press, Oxford 1964.

P. Koosis: Introduction to H_p Spaces, University Press, Cambridge 1980.

G. Polya and G. Latta: Complex Variables, John Wiley & Sons, New York, 1974.

Title of the course: Codes and symmetric structures

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tamás Szőnyi

Department(s): Department of Computer Science

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Error-correcting codes; important examples: Hamming, BCH (Bose, Ray-Chaudhuri, Hocquenheim) codes. Bounds for the parameters of the code: Hamming bound and perfect codes, Singleton bound and MDS codes. Reed-Solomon, Reed-Muller codes. The Gilbert-Varshamov bound. Random codes, explicit asymptotically good codes (Forney's concatenated codes, Justesen codes). Block designs t-designs and their links with perfect codes. Binary and ternary Golay codes and Witt designs. Fisher's inequality and its variants. Symmetric designs, the Bruck-Chowla-Ryser condition. Constructions (both recursive and direct) of block designs.

Textbook: none

Further reading:

P.J. Cameron, J.H. van Lint: Designs, graphs, codes and their links Cambridge Univ. Press, 1991.

J. H. van Lint: Introduction to Coding theory, Springer, 1992.

J. H. van Lint, R.J. Wilson, A course in combinatorics, Cambridge Univ. Press, 1992; 2001

Title of the course: Combinatorial algorithms I.

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): Tibor Jordán

Department(s): Department of Operations Research

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Search algorithms on graphs, maximum adjacency ordering, the algorithm of Nagamochi and Ibaraki. Network flows. The Ford Fulkerson algorithm, the algorithm of Edmonds and Karp, the preflow push algorithm. Circulations. Minimum cost flows. Some applications of flows and circulations. Matchings in graphs. Edmonds` algorithm, the Gallai Edmonds structure theorem. Factor critical graphs. T-joins, f-factors. Dinamic programming. Minimum cost

arborescences.

Textbook:

A. Frank, T. Jordán, Combinatorial algorithms, lecture notes.

Further reading:

Title of the course: Combinatorial algorithms II.

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tibor Jordán

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Connectivity of graphs, sparse certificates, ear decompositions. Karger`s algorithm for computing the edge connectivity. Chordal graphs, simplicial ordering. Flow equivalent trees, Gomory Hu trees. Tree width, tree decomposition. Algorithms on graphs with small tree width. Combinatorial rigidity. Degree constrained orientations. Minimum cost circulations.

Textbook:

A. Frank, T. Jordán, Combinatorial algorithms, lecture notes.

Further reading:

Title of the course: Combinatorial Geometry

Number of contact hours per week: 2+1

Credit value: 2+2

Course coordinator: György Kiss

Department: Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Combinatorial properties of finite projective and affine spaces. Collineations and polarities, conics, quadrics, Hermitian varieties, circle geometries, generalized quadrangles.

Point sets with special properties in Euclidean spaces. Convexity, Helly-type theorems, transversals.

Polytopes in Euclidean, hyperbolic and spherical geometries. Tilings, packings and coverings. Density problems, systems of circles and spheres.

Textbook: none

Further reading:

1. Boltyanski, V., Martini, H. and Soltan, P.S.: Excursions into Combinatorial Geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1997.

2. Coxeter, H.S.M.: Introduction to Geometry, John Wiley & Sons, New York, 1969.

3. Fejes Tóth L.: Regular Figures, Pergamon Press, Oxford-London-New York-Paris, 1964.

Title of the course: Combinatorial number theory.

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): András Sárközy

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination

Prerequisites: Number theory 2

A short description of the course:

Brun's sieve and its applications. Schnirelmann's addition theorems, the primes form an additive basis. Additive and multiplicative Sidon sets. Divisibility properties of sequences, primitive sequences. The "larger sieve", application. Hilbert cubes in dense sequences, applications. The theorems of van der Waerden and Szemeredi on arithmetic progressions. Schur's theorem on the Fermat congruence.

Textbook: none

Further reading:

H. Halberstam, K. F. Roth: Sequences.

C. Pomerance, A. Sárközy: Combinatorial Number Theory (in: Handbook of Combinatorics)

P. Erdős, J. Surányi: Topics in number theory.

Title of the course: Combinatorial structures and algorithms

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): Tibor Jordán

Department(s): Department of Operations Research

Evaluation: tutorial mark

Prerequisites:

A short description of the course:

Solving various problems from combinatorial optimization, graph theory, matroid theory, and combinatorial geometry.

Textbook: none

Further reading: L. Lovász, Combinatorial problems and exercises, North Holland 1979.

Title of the course: Commutative algebra

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): József Pelikán

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination and tutorial mark

Prerequisites: Rings and Algebras

A short description of the course:

Ideals. Prime and maximal ideals. Zorn's lemma. Nilradical, Jacobson radical. Prime spectrum.

Modules. Operations on submodules. Finitely generated modules. Nakayama's lemma. Exact sequences. Tensor product of modules.

Noetherian rings. Chain conditions for mudules and rings. Hilbert's basis theorem. Primary ideals. Primary decomposition, Lasker-Noether theorem. Krull dimension. Artinian rings.

Localization. Quotient rings and modules. Extended and restricted ideals.

Integral dependence. Integral closure. The 'going-up' and 'going-down' theorems. Valuations. Discrete valuation rings. Dedekind rings. Fractional ideals.

Algebraic varieties. 'Nullstellensatz'. Zariski-topology. Coordinate ring. Singular and regular points. Tangent space.

Dimension theory. Various dimensions. Krull's principal ideal theorem. Hilbert-functions. Regular local rings. Hilbert's theorem on syzygies.

Textbook: none

Further reading:

Atiyah, M.F.–McDonald, I.G.: Introduction to Commutative Algebra. Addison–Wesley, 1969.

Title of the course: Complex Functions

Number of contact hours per week: 3+2

Credit value: 3+3

Course coordinator(s): Gábor Halász

Department(s): Department of Analysis

Evaluation: oral examination and tutorial mark

Prerequisites: Analysis 3 (BSc)

A short description of the course:

Complex differentiation. Power series. Elementary functions. Cauchy’s integral theorem and integral formula. Power series representation of regular functions. Laurent expansion. Isolated singularities. Maximum principle. Schwarz lemma and its applications. Residue theorem. Argument principle and its applications. Sequences of regular functions. Linear fractional transformations. Riemann’s conformal mapping theorem. Extension to the boundary. Reflection principle. Picard’s theorem. Mappings of polygons. Functions with prescribed singularities. Integral functions with prescribed zeros. Functions of finite order. Borel exceptional values. Harmonic functions. Dirichlet problem for a disc.

Textbook:

Further reading:

L. Ahlfors: Complex Analysis, McGraw-Hill Book Company, 1979.

Title of the course: Complex manifolds

Number of contact hours per week: 3+2

Credit value: 4+3

Course coordinator(s): Róbert Szőke

Department(s): Department of Analysis

Evaluation: oral or written examination and tutorial mark

Prerequisites: complex analysis (BSc)

real analysis and algebra (BSc)

Some experience with real manifolds and differential forms is useful.

A short description of the course:

Complex and almost complex manifolds, holomorphic fiber bundles and vector bundles, Lie groups and transformation groups, cohomology, Serre duality, quotient and submanifolds, blowup, Hopf-, Grassmann and projective algebraic manifolds, Weierstrass' preparation and division theorem, analytic sets, Remmert-Stein theorem, meromorphic functions, Siegel, Levi and Chow's theorem, rational functions.

Objectives of the course: the intent of the course is to familiarize the students with the most important methods and objects of the theory of complex manifolds and to do this as simply as possible. The course completely avoids those abstract concepts (sheaves, coherence, sheaf cohomology) that are subjects of Ph.D. courses. Using only elementary methods (power series, vector bundles, one dimensional cocycle) and presenting many examples, the course introduces the students to the theory of complex manifolds and prepares them for possible future Ph.D. studies.

Textbook: Klaus Fritzsche, Hans Grauert: From holomorphic functions to complex manifolds, Springer Verlag, 2002

Further reading:

K. Kodaira: Complex manifolds and deformations of complex structures, Springer Verlag, 2004

1.Huybrechts: Complex geometry: An introduction, Springer Verlag, 2004

Title of the course: Complexity theory

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): Vince Grolmusz

Department(s): Department of Computer Science

Evaluation: oral examination and tutorial mark

Prerequisites:

A short description of the course: finite automata, Turing machines, Boolean circuits. Lower bounds to the complexity of algorithms. Communication complexity. Decision trees, Ben-Or’s theorem, hierarchy theorems. Savitch theorem. Oracles. The polynomial hierarchy. PSPACE. Randomized complexity classes. Pseudorandomness. Interactive protocols. IP=PSPACE. Approximability theory. The PCP theorem. Parallel algorithms. Kolmogorov complexity.

Textbook: László Lovász: Computational Complexity (ftp://ftp.cs.yale.edu/pub/lovasz.pub/complex.ps.gz)

Further reading:

Papadimitriou: Computational Complexity (Addison Wesley, 1994)

Cormen. Leiserson, Rivest, Stein: Introduction to Algorithms; MIT Press and McGraw-Hill.

Title of the course: Complexity theory seminar

Number of contact hours per week: 0+2

Credit value: 2

Course coordinator(s): Vince Grolmusz

Department(s): Department of Computer Science

Evaluation: oral examination or tutorial mark

Prerequisites: Complexity theory

A short description of the course: Selected papers are presented in computational complexity theory

Textbook: none

Further reading:

STOC and FOCS conference proceedings

The Electronic Colloquium on Computational Complexity (http://eccc.hpi-web.de/eccc/)

Title of the course: Computational methods in operations research

Number of contact hours per week: 0+2

Credit value: 0+3

Course coordinator(s): Gergely Mádi-Nagy

Department(s): Department of Operations Research

Evaluation: tutorial mark

Prerequisites: -

A short description of the course:

Implementation questions of mathematical programming methods.

Formulation of mathematical programming problems, and interpretation of solutions: progress from standard input/output formats to modeling tools.

The LINDO and LINGO packages for linear, nonlinear, and integer programming. The CPLEX package for linear, quadratic, and integer programming.

Modeling tools: XPRESS, GAMS, AMPL.

Textbook: none

Further reading: Maros, I.: Computational Techniques of the Simplex Method, Kluwer Academic Publishers, Boston, 2003

Title of the course: Continuous Optimization

Number of contact hours per week: 3+2

Credit value: 3+3

Course coordinator(s): Tibor Illés

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course: Linear inequality systems: Farkas lemma and other alternative theorems, The duality theorem of linear programming, Pivot algorithms (criss-cross, simplex), Interior point methods, Matrix games: Nash equilibrium, Neumann theorem on the existence of mixed equilibrium, Convex optimization: duality, separability, Convex Farkas theorem, Kuhn-Tucker-Karush theorem, Nonlinear programming models, Stochastic programming models.

Textbook: none

Further reading:

1. Katta G. Murty: Linear Programming. John Wiley & Sons, New York, 1983.

2. Vašek Chvátal: Linear Programming. W. H. Freeman and Company, New York, 1983.

3. C. Roos, T. Terlaky and J.-Ph. Vial: Theory and Algorithms for Linear Optimization: An Interior Point Approach. John Wiley & Sons, New York, 1997.

4. Béla Martos: Nonlinear Programming: Theory and Methods. Akadémiai Kiadó, Budapest, 1975.

5. M. S. Bazaraa, H. D. Sherali and C. M. Shetty: Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, New York, 1993.

6. J.-B. Hiriart-Urruty and C. Lemaréchal: Convex Analysis and Minimization Algorithms I-II. Springer-Verlag, Berlin, 1993.

Title of the course: Convex Geometry

Number of contact hours per week: 4+2

Credit value: 6+3

Course coordinator(s): Károly Böröczky, Jr.

Department(s): Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Convex polytopes, Euler and Dehn–Sommerville formulas, upper bound theorem.

Mean projections. Isoperimetric, Brunn-Minkowski, Alexander-Fenchel, Rogers–Shephard and Blaschke-Santalo inequalities.

Lattices in Euclidean spaces. Successive minima and covering radius. Minkowski, Minkowski–Hlawka and Mahler theorems. Critical lattices and finiteness theorems. Reduced basis.

Textbook: none

Further reading:

1) B. Grünbaum: Convex polytopes, 2nd edition, Springer-Verlag, 2003.

2) P.M. Gruber: Convex and Discrete Geometry, Springer-Verlag, 2006.

3) P.M. Gruber, C.G. Lekkerkerker: Geometry of numbers, North-Holland, 1987.

Title of the course: Cryptography

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): István Szabó

Department(s): Department of Probability Theory and Statistics

Evaluation: C type examination

Prerequisites: Probability and statistics

A short description of the course:

Data Security in Information Systems. Confidentiality, Integrity, Authenticity, Threats (Viruses, Covert Channels), elements of the Steganography and Cryptography;

Short history of Cryptography (Experiences, Risks);

Hierarchy in Cryptography: Primitives, Schemes, Protocols, Applications;

Random- and Pseudorandom Bit-Generators;

Stream Ciphers: Linear Feedback Shift Registers, Stream Ciphers based on LFSRs, Linear Complexity, Stream Ciphers in practice (GSM-A5, Bluetooth-E0, WLAN-RC4), The NIST Statistical Test Suite;

Block Ciphers: Primitives (DES, 3DES, IDEA, AES), Linear and Differential Cryptanalysis;

Public-Key Encryption: Primitives (KnapSack, RSA, ElGamal public-key encryption, Elliptic curve cryptography,…), Digital Signatures, Types of attacks on PKS (integer factorisation problem, Quadratic/Number field sieve factoring, wrong parameters,…);

Hash Functions and Data Integrity: Requirements, Standards and Attacks (birthday, collisions attacks);

Cryptographic Protocols: Modes of operations, Key management protocols, Secret sharing, Internet protocols (SSL-TLS, IPSEC, SSH,…)

Cryptography in Information Systems (Applications): Digital Signatures Systems (algorithms, keys, ETSI CWA requirements, Certification Authority, SSCD Protection Profile, X-509v3 Certificate,…), Mobile communications (GSM), PGP, SET,…;

Quantum Cryptography (quantum computation, quantum key exchange, quantum teleportation).

Textbook: none

Further reading:

Bruce Schneier: Applied Cryptography. Wiley, 1996

Alfred J. Menezes, Paul C. van Oorshchor, Scott A. Vanstone: Handbook of Applied Cryptography, CRC Press, 1997, http://www.cacr.math.uwaterloo.ca/hac/

Title of the course: Current topics in algebra

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator: Emil Kiss

Department: Department of Algebra and Number Theory

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

This subject of this course is planned to change from year to year. Some possible topics: algebraic geometry, elliptic curves, p-adic numbers, valuation theory, Dedekind-domains, binding categories.

Textbook: none

Further reading:

depends on the subject

Title of the course: Data mining

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator: András Lukács

Department: Department of Computer Science

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Basic concepts and methodology of knowledge discovery in databases and data mining. Frequent pattern mining, association rules. Level-wise algorithms, APRIORI. Partitioning and Toivonen algorithms. Pattern growth methods, FP-growth. Hierarchical association rules. Constraints handling. Correlation search.

Dimension reduction. Spectral methods, low-rank matrix approximation. Singular value decomposition. Fingerprints, fingerprint based similarity search.

Classification. Decision trees. Neural networks. k-NN, Bayesian methods, kernel methods, SVM.

Clustering. Partitioning algorithms, k-means. Hierarchical algorithms. Density and link based clustering, DBSCAN, OPTICS. Spectral clustering.

Applications and implementation problems. Systems architecture in data mining. Data structures.

Textbook:

Further reading:

Jiawei Han és Micheline Kamber: Data Mining: Concepts and Techniques, Morgan Kaufmann Publishers, 2000, ISBN 1558604898,

Pang-Ning Tan, Michael Steinbach, Vipin Kumar: Introduction to Data Mining, Addison-Wesley, 2006, ISBN 0321321367.

T. Hastie, R. Tibshirani, J. H. Friedman: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer-Verlag, 2001.

Title of the course: Descriptive set theory

Number of contact hours per week: 3+2

Credit value: 4+3

Course coordinator(s): Miklos Laczkovich

Department(s): Department of Analysis

Evaluation: oral or written examination and tutorial mark

Prerequisites: Analysis 4,

Introduction to topology

A short description of the course:

Basics of general topology. The Baire property. The tranfinite hierarchy of Borel sets. The Baire function classes. The Suslin operation. Analytic and coanalytic sets. Suslin spaces. Projective sets.

Textbook: none

Further reading:

K. Kuratowski: Topology I, Academic Press, 1967.

A. Kechris: Classical descriptive set theory, Springer, 1998.

Title of the course: Design, analysis and implementation of algorithms and data structures I

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): Zoltán Király

Department(s): Department of Computer Science

Evaluation: oral examination

Prerequisites: Algorithms I

A short description of the course:

Maximum adjacency ordering and its applications. Sparse certificates for connectivity. Minimum cost arborescence. Degree constrained orientations of graphs. 2-SAT. Tree-width, applications. Gomory-Hu tree and its application. Steiner tree and traveling salesperson.

Minimum cost flow and circulation, minimum mean cycle.

Matching in non-bipartite graphs, factor-critical graphs, Edmonds’ algorithm. Structure theorem of Gallai and Edmonds. T-joins, the problem of Chinese postman.

On-line algorithms, competitive ratio.

Textbook: none

Further reading:

T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein: Introduction to Algorithms, McGraw-Hill, 2002.

A. Schrijver: Combinatorial Optimization, Springer-Verlag, 2002.

Robert Endre Tarjan: Data Structures and Network Algorithms , Society for Industrial and Applied Mathematics, 1983.

Berg-Kreveld-Overmars-Schwarzkopf: Computational Geometry: Algorithms and Applications , Springer-Verlag, 1997.

Title of the course: Design, analysis and implementation of algorithms and data structures II

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Zoltán Király

Department(s): Department of Computer Science

Evaluation: oral examination

Prerequisites: Design, analysis and implementation of algorithms and data structures I

A short description of the course:

Data structures for the UNION-FIND problem. Pairing and radix heaps. Balanced and self-adjusting search trees.

Hashing, different types, analysis. Dynamic trees and their applications.

Data structures used in geometric algorithms: hierarchical search trees, interval trees, segment trees and priority search trees.

Textbook: none

Further reading:

T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein: Introduction to Algorithms, McGraw-Hill, 2002.

A. Schrijver: Combinatorial Optimization, Springer-Verlag, 2002.

Robert Endre Tarjan: Data Structures and Network Algorithms , Society for Industrial and Applied Mathematics, 1983.

Berg-Kreveld-Overmars-Schwarzkopf: Computational Geometry: Algorithms and Applications , Springer-Verlag, 1997.

Title of the course: Differential Geometry I

Number of contact hours per week: 2+2

Credit value: 2+3

Course coordinator(s): László Verhóczki (associate professor)

Department(s): Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Smooth parameterized curves in the n-dimensional Euclidean space Rⁿ. Arc length parameterization. Distinguished Frenet frame. Curvature functions, Frenet formulas. Fundamental theorem of the theory of curves. Signed curvature of a plane curve. Four vertex theorem. Theorems on total curvatures of closed curves.

Smooth hypersurfaces in Rⁿ. Parameterizations. Tangent space at a point. First fundamental form. Normal curvature, Meusnier’s theorem. Weingarten mapping, principal curvatures and directions. Christoffel symbols. Compatibility equations. Theorema egregium. Fundamental theorem of the local theory of hypersurfaces. Geodesic curves.

Textbook:

M. P. do Carmo: Differential geometry of curves and surfaces. Prentice Hall, Englewood
Cliffs, 1976.

Further reading:

B. O’Neill: Elementary differential geometry. Academic Press, New York, 1966.

Title of the course: Differential Geometry II

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): László Verhóczki

Department(s): Department of Geometry

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Differentiable manifolds. Smooth mappings between manifolds. Tangent space at a point. Tangent bundle of a manifold. Lie bracket of two smooth vector fields. Submanifolds. Covariant derivative. Parallel transport along a curve. Riemannian manifold, Levi-Civita connection. Geodesic curves. Riemannian curvature tensor field. Spaces of constant curvature. Differential forms. Exterior product. Exterior derivative. Integration of differential forms. Volume. Stokes’ theorem.

Textbooks:

1. F. W. Warner: Foundations of differentiable manifolds and Lie groups. Springer-Verlag
New York, 1983.

2. M. P. do Carmo: Riemannian geometry. Birkhäuser, Boston, 1992.

Further reading:

Title of the course: Differential Topology (basic material)

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): András Szűcs

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: Algebraic Topology course in BSC

A short description of the course:

Morse theory, Pontrjagin construction, the first three stable homotopy groups of spheres,

Proof of the Poincare duality using Morse theory, immersion theory.

Textbook:

Further reading:

M. W. Hirsch: Differential Topology, Springer-Verlag, 1976.

Title of the course: Differential Topology Problem solving

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): András Szűcs

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: BSc Algebraic Topology Course

A short description of the course:

See at the courses of Differential and Algebraic Topology of the basic material

Textbook:

Further reading:

1) J. W. Milnor J. D Stasheff: Characteristic Classes, Princeton, 1974.

2) R. E. Stong: Notes on Cobordism theory, Princeton 1968.

Title of the course: Discrete Dynamical Systems

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Zoltán Buczolich

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: Measure and integration theory (BSc Analysis 4)

A short description of the course:

Topologic transitivity and minimality. Omega limit sets. Symbolic Dynamics. Topologic Bernoulli shift. Maps of the circle. The existence of the rotation number. Invariant measures. Krylov-Bogolubov theorem. Invariant measures and minimal homeomorphisms. Rotations of compact Abelian groups. Uniquely ergodic transformations and minimality. Unimodal maps. Kneading sequence. Eventually periodic symbolic itinerary implies convergence to periodic points. Ordering of the symbolic itineraries. Characterization of the set of the itineraries. Equivalent definitions of the topological entropy. Zig-zag number of interval maps. Markov graphs. Sharkovskii’s theorem. Foundations of the Ergodic theory. Maximal and Birkhoff ergodic theorem.

Textbook: none

Further reading:

A. Katok, B.Hasselblatt: Introduction to the modern theory of dynamical systems.Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press,Cambridge, 1995.

W. de Melo, S. van Strien, One-dimensional dynamics, Springer Verlag, New York (1993).

I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer Verlag, New York, (1981).

Title of the course: Discrete Geometry

Number of contact hours per week: 3+2

Credit value: 4+3

Course coordinator(s): Károly Bezdek

Department(s): Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Packings and coverings in E². Dowker theorems. The theorems of L. Fejes Tóth and Rogers on densest packing of translates of a convex or centrally symmetric convex body. Homogeneity questions. Lattice-like arrangements. Homogeneous packings (with group actions). Space claim, separability.

Packings and coverings in (Euclidean, hyperbolic or spherical space) A^d. Problems with the definition of density. Densest circle packings (spaciousness), and thinnest circle coverings in A². Tammes problem. Solidity. Rogers’ density bound for sphere packings in E^d. Clouds, stable systems and separability. Densest sphere packings in A³. Tightness and edge tightness. Finite systems. Problems about common transversals.

Textbook: none

Further reading:

1. Fejes Tóth, L.: Regular figures, Pergamon Press, Oxford–London–New York–Paris, 1964.

2. Fejes Tóth, L.: Lagerungen in der Ebene auf der Kugel und im Raum, Springer-Verlag,

Berlin–Heidelberg–NewYork, 1972.

3. Rogers, C. A.: Packing and covering, Cambridge University Press, 1964.

4. Böröczky, K. Jr.: Finite packing and covering, Cambridge Ubiversity Press, 2004.

Title of the course: Discrete Mathematics

Number of contact hours per week: 2+2.

Credit value: 2+3

Course coordinator(s): László Lovász

Department(s): Department of Computer Science

Evaluation: oral or written examination and tutorial grade

Prerequisites:

A short description of the course:

Graph Theory: Colorings of graphs and.hypergraphs, perfect graphs.Matching Theory. Multiple connectivity. Strongly regular graphs, integrality condition and its application. Extremal graphs. Regularity Lemma. Planarity, Kuratowski’s Theorem, drawing graphs on surfaces, minors, Robertson-Seymour Theory.

Fundamental questions of enumerative combinatorics. Generating functions, inversion formulas for partially ordered sets, recurrences. Mechanical summation.Classical counting problems in graph theory, tress, spanning trees, number of 1-factors.

Randomized methods: Expectation and second moment method. Random graphs, threshold functions.

Applications of fields: the linear algebra method, extremal set systems. Finite fields, error correcting codes, perfect codes.

Textbook: none

Further reading:

J. H. van Lint, R.J. Wilson, A course in combinatorics, Cambridge Univ. Press, 1992; 2001.

L. Lovász: Combinatorial Problems and Exercises, AMS, Providence, RI, 2007

R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics,

Title of the course: Discrete Mathematics II

Number of contact hours per week: 4+0

Credit value: 6

Course coordinator(s): Tamás Szőnyi

Department(s): Department of Computer Science

Evaluation: oral examination

Prerequisites: Discrete Mathematics I

A short description of the course:

Probabilistic methods: deterministic improvement of a random object. Construction of graphs with large girth and chromatic number.

Random graphs: threshold function, evolution around p=logn/n. Pseudorandom graphs.

Local lemma and applications.

Discrepancy theory. Beck-Fiala theorem.

Spencer’s theorem. Fundamental theorem on the Vapnik-Chervonenkis dimension.

Extremal combinatorics

Non- bipartite forbidden subgraphs: Erdős-Stone-Simonovits and Dirac theorems.

Bipartite forbidden subgraphs: Turan number of paths and K(p,q). Finite geometry and algebraic constructions.

Szemerédi’s regularity lemma and applications. Turán-Ramsey type theorems.

Extremal hypergraph problems: Turán’s conjecture.

Textbook:

Further reading:

Alon-Spencer: The probabilistic method, Wiley 2000.

Title of the course: Discrete optimization

Number of contact hours per week: 3+2

Credit value: 3+3

Course coordinator: András Frank

Department: Dept. Of Operations research

Evaluation: oral exam + tutorial mark

Prerequisites:

A short description of the course:

Basic notions of graph theory and matroid theory, properties and methods (matchings, flows and circulations, greedy algorithm). The elements of polyhedral combinatorics (totally unimodular matrices and their applications). Main combinatorial algorithms (dynamic programming, alternating paths, Hungarian method). The elements of integer linear programming (Lagrangian relaxation, branch-and-bound).

Textbook:

András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:

W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial Optimization, John Wiley and Sons, 1998.

B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms, Springer, 2000.

E. Lawler, Kombinatorikus Optimalizálás: hálózatok és matroidok, Műszaki Kiadó, 1982. (Combinatorial Optimization: Networks and Matroids).

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24 of the series Algorithms and Combinatorics.

R. K. Ahuja, T. H. Magnanti, J. B. Orlin: Network flows: Theory, Algorithms and Applications, Elsevier North-Holland, Inc., 1989

Title of the course: Discrete parameter martingales

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): Tamás F. Móri

Department(s): Department of Probability Theory and Statistics

Evaluation: oral examination

Prerequisites: Probability and statistics

A short description of the course:

Almost sure convergence of martingales. Convergence in L_p, regular martingales.

Regular stopping times, Wald’s theorem.

Convergence set of square integrable martingales.

Hilbert space valued martingales.

Central limit theory for martingales.

Reversed martingales, U-statistics, interchangeability.

Applications: martingales in finance; the Conway algorithm; optimal strategies in favourable games; branching processes with two types of individuals.

Textbook: none

Further reading:

Y. S. Chow – H. Teicher: Probability Theory – Independence, Interchangeability, Martingales. Springer, New York, 1978.

J. Neveu: Discrete-Parameter Martingales. North-Holland, Amsterdam, 1975.

Title of the course: Dynamical Systems

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Zoltán Buczolich

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: Differential equations (BSc)

A short description of the course:

Contractions, fixed point theorem. Examples of dynamical systems: Newton’s method, interval maps, quadratic family, differential equations, rotations of the circle. Graphic analysis. Hyperbolic fixed points. Cantor sets as hyperbolic repelleres, metric space of code sequences. Symbolic dynamics and coding. Topologic transitivity, sensitive dependence on the initial conditions, chaos/chaotic maps, structural stability, period three implies chaos. Schwarz derivative. Bifuraction theory. Period doubling. Linear maps and linear differential equations in the plane. Linear flows and translations on the torus. Conservative systems.

Textbook: none

Further reading:

B. Hasselblatt, A. Katok: A first course in dynamics. With a panorama of recentdevelopments. Cambridge University Press, New York, 2003.

A. Katok, B.Hasselblatt: Introduction to the modern theory of dynamical systems.Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press,Cambridge, 1995.

Robert L. Devaney: An introduction to chaotic dynamical systems. Second edition. AddisonWesley Studies in Nonlinearity. AddisonWesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989.

Title of the course: Dynamical systems and differential equations

Number of contact hours per week: 4+2

Credit value: 6+3

Course coordinator(s): Péter Simon

Department(s): Dept. of Appl. Analysis and Computational Math.

Evaluation: oral or written examination and tutorial mark

Prerequisites: Differential equations (BSc)

A short description of the course:

Topological equivalence, classification of linear systems. Poincaré normal forms, classification of nonlinear systems. Stable, unstable, centre manifolds theorems, Hartman - Grobman theorem. Periodic solutions and their stability. Index of two-dimensional vector fields, behaviour of trajectories at infinity. Applications to models in biology and chemistry. Hamiltonian systems. Chaos in the Lorenz equation.

Bifurcations in dynamical systems, basic examples. Definitions of local and global bifurcations. Saddle-node bifurcation, Andronov-Hopf bifurcation. Two-codimensional bifurcations. Methods for finding bifurcation curves. Structural stability. Attractors.

Discrete dynamical systems. Classification according to topological equivalence. 1D maps, the tent map and the logistic map. Symbolic dynamics. Chaotic systems. Smale horseshoe , Sharkovski’s theorem. Bifurcations.

Textbook: none

Further reading:

L. Perko, Differential Equations and Dynamical systems, Springer

Title of the course: Dynamics in one complex variable

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): István Sigray

Department(s): Department of Analysis

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Julia és Fatou sets. Smooth Julia sets. Attractive fixpoints, Koenigs linearization theorem. Superattractive fixpoints Bötkher theorem. Parabolic fixpoints, Leau-Fatou theorem. Cremer points és Siegel discs. Holomorphic fixpoint formula. Dense subsets of the Julia set.. Herman rings. Wandering domains. Iteration of Polynomials. The Mandelbrot set. Root finding by iteration. Hyperbolic mapping. Local connectivity.

Textbook:

John Milnor: Dynamics in one complex variable, Stony Brook IMS Preprint #1990/5

Further reading:

M. Yu. Lyubich: The dynamics of rational transforms, Russian Math Survey, 41 (1986) 43–117

A. Douady: Systeme dynamique holomorphes, Sem Bourbaki , Vol 1982/83, 39-63, Asterisque, 105–106

Title of the course: Ergodic theory

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Zoltán Buczolich

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: : Measure and integration theory (BSc Analysis 4) ,

Functional analysis 1.

A short description of the course:

Examples. Constructions. Von Neumann L2 ergodic theorem. Birkhoff-Khinchin pointwise ergodic theorem. Poincaré recurrence theorem and Ehrenfest’s example. Khinchin’s theorem about recurrence of sets. Halmos’s theorem about equivalent properties to recurrence. Properties equivalent to ergodicity. Measure preserving property and ergodicity of induced maps. Katz’s lemma. Kakutani-Rokhlin lemma. Ergodicity of the Bernoulli shift, rotations of the circle and translations of the torus. Mixing (definitions). The theorem of Rényi about strongly mixing transformations. The Bernoulli shift is strongly mixing. The Koopman von Neumann lemma. Properties equivalent to weak mixing. Banach’s principle. The proof of the Ergodic Theorem by using Banach’s principle. Differentiation of integrals. Wiener’s local ergodic theorem. Lebesgue spaces and properties of the conditional expectation. Entropy in Physics and in information theory. Definition of the metric entropy of a partition and of a transformation. Conditional information and entropy. ``Entropy metrics”. The conditional expectation as a projection in L2. The theorem of Kolmogorv and Sinai about generators. Krieger’s theorem about generators (without proof).

Textbook: none

Further reading:

K. Petersen, Ergodic Theory,Cambridge Studies in Advanced Mathematics 2, Cambridge University Press, (1981).

I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer Verlag, New York, (1981).

Title of the course: Exponential sums in number theory.

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): András Sárközy

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Additive and multiplicative characters, their connection, applications. Vinogradov's lemma and its dual. Gaussian sums. The Pólya-Vinogradov inequality. Estimate of the least quadratic nonresidue. Kloosterman sums. The arithmetic and character form of the large sieve, applications. Irregularities of distribution relative to arithmetic progressions, lower estimate of character sums. Uniform distribution. Weyl's criterion. Discrepancy. The Erdős-Turán inequality. Van der Corput's method.

Textbook: none

Further reading:

I. M. Vinogradov: Elements of number theory

L. Kuipers, H. Niederreiter: Uniform Distribution of Sequences.

S. W. Graham, G. Kolesnik: Van der Corput’s Method of Exponential Sums.

H. Davenport: Multiplicative Number Theory.

Title of the course: Finite Geometries

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator: György Kiss (associate professor)

Department: Department of Geometry

Evaluation: oral examination

Prerequisites:

A short description of the course:

The axiomams of projective and affine planes, examples of finite planes, non-desarguesian planes. Collineations, configurational theorems, coordinatization of projective planes. Higher dimensional projective spaces.

Arcs, ovals, Segre’s Lemma of Tangents. Estimates on the number of points on an algebraic curve. Blocking sets, some applications of the Rédei polynomial. Arcs, caps and ovoids in higher dimensional spaces.

Coverings and packings, linear complexes, generalized polygons. Hyperovals.

Some applications of finite geometries to graph theory, coding theory and cryptography.

Textbook: none

Further reading:

1. Hirschfeld, J:W.P.: Projective Geometries over Finite Fields, Clarendon Press, Oxford,

1999.

2. Hirschfeld, J.W.P.: Finite Projective Spaces of Three Dimensions, Clarendon Press,

Oxford, 1985.

Title of the course: Fourier Integral

Number of contact hours per week: 2+1

Credit value: 2+1

Course coordinator(s): Gábor Halász

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: Complex Functions (BSc),

Analysis IV. (BSc),

Probability 2. (BSc)

A short description of the course:

Fourier transform of functions in L_1. Riemann Lemma. Convolution in L_1. Inversion formula. Wiener’s theorem on the closure of translates of L_1 functions. Applications to Wiener’s general Tauberian theorem and special Tauberian theorems.

Fourier transform of complex measures. Characterizing continuous measures by its Fourier transform. Construction of singular measures.

Fourier transform of functions in L_2. Parseval formula. Convolution in L_2. Inversion formula. Application to non-parametric density estimation in statistics.

Young-Hausdorff inequality. Extension to L_p. Riesz-Thorin theorem. Marczinkiewicz interpolation theorem.

Application to uniform distribution. Weyl criterion, its quantitative form by Erdős-Turán. Lower estimation of the discrepancy for disks.

Characterization of the Fourier transform of functions with bounded support. Paley-Wiener theorem.

Phragmén-Lindelöf type theorems.

Textbook:

Further reading:

E.C. Titchmarsh: Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1937.

A. Zygmund: Trigonometric Series, University Press, Cambridge, 1968, 2 volumes

R. Paley and N. Wiener: Fourier Transforms in the Complex Domain, American Mathematical Society, New York, 1934.

J. Beck and W.L. Chen: Irregularities of Distribution, University Press, Cambridge, 1987.

Title of the course: Function Series

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): János Kristóf

Department: Dept. of Appl. Analysis and Computational Math.

Evaluation: oral examination

Prerequisites:

A short description of the course:

Pointwise and L^2 norm convergence of orthogonal series. Rademacher-Menshoff theorem. Weyl-sequence. Pointwise convergence of trigonometric Fourier-series. Dirichlet integral. Riemann-Lebesgue lemma. Riemann’s localization theorem for Fourier-series. Local convergence theorems. Kolmogorov’s counterexample. Fejér’s integral. Fejér’s theorem. Carleson’s theorem.

Textbooks:

Bela Szokefalvi-Nagy: Introduction to real functions and orthogonal expansions,

Natanszon: Constructive function theory

Title of the course: Functional analysis II

Number of contact hours per week: 1+2

Credit value: 1+2

Course coordinator(s): Sebestyén Zoltán

Department(s): Department of Appl. Analysis and Computational Math.

Evaluation: oral examination

Prerequisites: Algebra IV

Analysis IV

A short description of the course:

Banach-Alaoglu Theorem. Daniel-Stone Theorem. Stone-Weierstrass Theorem. Gelfand Theory, Representation Theory of Banach algebras.

Textbook:

Riesz–Szőkefalvi-Nagy: Functional analysis

Further reading:

W. Rudin: Functional analysis

F.F. Bonsall-J. Duncan: Complete normed algebras

Title of the course: Game Theory

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tibor Illés

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Matrix games. Optimal strategies for matrix games with saddle point. Mixed strategies, expected yield. Neumann minimax theorem. Solving matrix games with linear programming. Nash equilibrium. Sperner lemma. The first and second Knaster-Kuratowski-Mazurkiewicz theorems. The Brower and Kakutani fixed-point theorems. Shiffmann minimax theorem. Arrow-Hurwitz and Arrow-Debreu theorems. The Arrow-Hurwitz-Uzawa condition. The Arrow-Hurwitz and Uzawa algorithms. Applications of games in environment protection, health sciences and psichology.

Textbook: none

Further reading:

Forgó F., Szép J., Szidarovszky F., Introduction to the theory of games: concepts, methods, applications, Kluwer Academic Publishers, Dordrecht, 1999.

Osborne, M. J., Rubinstein A., A course in game theory, The MIT Press, Cambridge, 1994.

J. P. Aubin: Mathematical Methods of Game and Economic Theor. North-Holland, Amsterdam, 1982.

Title of the course: Geometric algorithms

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Katalin Vesztergombi

Department(s): Department of Computer Science

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Convex hull algorithms in the plane and in higher dimensions.

Lower bounds: the Ben-Or theorem, moment curve, cyclic polyhedron. Decomposition of the plane by lines. Search of convex hull in the plane (in higher dimensions), search of large convex polygon (parabolic duality) . Point location queries in planar decomposition. Post office problem. Voronoi diagrams and Delaunay triangulations and applications. Randomized algorithms and estimations of running times.

Textbook: none

Further reading:

De Berg, Kreveld, Overmars, Schwartzkopf: Computational geometry. Algorithms and applications, Berlin, Springer 2000.

Title of the course: Geometric Foundations of 3D Graphics

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): György Kiss

Department(s): Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Planar representations of three-dimensional objects by methods of descriptive geometry (parallel and perspective projections). Matrix representations of affine transformations in Euclidean space. Homogeneous coordinates in projective space. Matrix representations of collineations of projective space. Coordinate systems and transformations applied in computer graphics. Position and orientation of a rigid body (in a fixed coordinate system). Approximation of parameterized boundary surfaces by triangulated polyhedral surfaces.

Three primary colors, tristimulus coordinates of a light beam. RGB color model. HLS color model. Geometric and photometric concepts of rendering. Radiance of a surface patch. Basic equation of photometry. Phong interpolation for the radiance of a surface patch illuminated by light sources. Digital description of a raster image. Representation of an object with triangulated boundary surfaces, rendering image by the ray tracing method. Phong shading, Gouraud shading.

Textbook: none

Further reading:

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes: Computer Graphics, Principles and Practice. Addison-Wesley, 1990.

Title of the course: Geometric Measure Theory

Number of contact hours per week: 3+2

Credit value: 4+3

Course coordinator(s): Tamás Keleti

Department(s): Department of Analysis

Evaluation: oral or written examination and tutorial mark

Prerequisites: Topics in Analysis

A short description of the course:

Hausdorff measure, energy and capacity. Dimensions of product sets. Projection theorems.

Covering theorems of Vitali and Besicovitch. Differentiation of measures.

The Kakeya problem, Besicovitch set, Nikodym set.

Dini derivatives. Contingent. Denjoy-Young-Saks theorem.

Textbook: none

Further reading:

P. Mattila: Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability. Cambridge University Press, Cambridge, 1995.

K. Falconer: Geomerty of Fractal Sets, Cambridge University Press, Cambridge, 1986.

S. Saks: Theory of the Integral, Dover, 1964

Title of the course: Geometric modeling

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): László Verhóczki

Department(s): Department of Geometry

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Solid modeling. Wire frames. Boundary representations. Implicit equations and parameterizations of boundary surfaces. Constructive Solid Geometry, Boolean set operations.

Representing curves and surfaces. Curve interpolation. Cubic Hermite polynomials. Fitting a composite Hermite curve through a set of given points. Curve approximation. Control polygon, blending functions. Bernstein polynomials. Bézier curves. De Casteljau algorithm. B-spline functions, de Boor algorithm. Application of weights, rational B-spline curves. Composite cubic B-spline curves, continuity conditions. Bicubic Hermite interpolation. Fitting a composite Hermite surface through a set of given points. Surface design. Bézier patches. Rational B-spline surfaces. Composite surfaces, continuity conditions.

Textbook: none

Further reading:

1. G. Farin: Curves and surfaces for computer aided geometric design. Academic Press,

Boston, 1988.

2. I. D. Faux and M. J. Pratt: Computational geometry for design and manufacture. Ellis

Horwood Limited, Chichester, 1979.

Title of the course: Geometry III

Number of contact hours per week: 3+2

Credit value: 3+2

Course coordinator(s): Balázs Csikós

Department(s): Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Projective geometry: projective space over a field, projective subspaces, dual space, collineations, the Fundamental Theorem of Projective Geometry. Cross ratio. The theorems of Pappus and Desargues, and their rôle in the axiomatic foundations of projective geometry. Quadrics: polarity, projective classification, conic sections.

Hyperbolic geometry: Minkowski spacetime, the hyperboloid model, the Cayley-Klein model, the conformal models of Poincaré. The absolute notion of parallelism, cycles, hyperbolic trigonometry.

Textbook:

M. Berger: Geometry I–II (Translated from the French by M. Cole and S. Levy).

Universitext, Springer–Verlag, Berlin, 1987.

Further reading:

Title of the course: Graph theory

Number of contact hours per week: 2+0.

Credit value: 3

Course coordinator(s): András Frank and Zoltán Király

Department(s): Dept. of Operations Research

Evaluation: oral exam

Prerequisites:

Short description of the course:

Graph orientations, connectivity augmentation. Matchings in not necessarily bipartite graphs, T-joins. Disjoint trees and arborescences. Disjoint paths problems. Colourings, perfect graphs.

Textbook:

András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:

W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial Optimization, John Wiley and Sons, 1998.

R. Diestel, Graph Theory, Springer Verlag, 1996.

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24 of the series Algorithms and Combinatorics.

Title of the course: Graph theory seminar

Number of contact hours per week: 0+2.

Credit value: 2

Course coordinator(s): László Lovász

Department(s): Department of Computer Science

Evaluation: type C exam

Prerequisites:

A short description of the course:

Study and presentation of selected papers

Textbook: none

Further reading:

Title of the course: Graph theory tutorial

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): András Frank and Zoltán Király

Department(s): Dept. of Operations Research

Evaluation: tutorial mark

Prerequisites:

A short description of the course:

Graph orientations, connectivity augmentation. Matchings in not necessarily bipartite graphs, T-joins. Disjoint trees and arborescences. Disjoint paths problems. Colourings, perfect graphs.

Textbook:

András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:

W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial Optimization, John Wiley and Sons, Icn., 1998.

R. Diestel, Graph Theory, Springer Verlag, 1996.

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24 of the series Algorithms and Combinatorics.

Title of the course: Groups and representations

Number of contact hours per week: 2+2

Credit value: 2+3

Course coordinator(s): Péter P. Pálfy

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Group actions, permutation groups, automorphism groups. Semidirect products. Sylow’s Theorems.

Finite p-groups. Nilpotent groups. Solvable groups, Phillip Hall’s Theorems.

Free groups, presentations, group varieties. The Nielsen-Schreier Theorem.

Abelian groups. The Fundamental Theorem of finitely generated Abelian groups. Torsionfree groups.

Linear groups and linear representations. Semisimple modules and algebras. Irreducible representations. Characters, orthogonality relations. Induced representations, Frobenius reciprocity, Clifford’s Theorems.

Textbook: none

Further reading:

D.J.S. Robinson: A course in the theory of groups, Springer, 1993

I.M. Isaacs: Character theory of finite groups, Academic Press, 1976

Title of the course: Integer Programming I

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tamás Király

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Basic modeling techniques. Hilbert bases, unimodularity, total dual integrality. General heuristic algorithms: Simulated annealing, Tabu search. Heuristic algorithms for the Traveling Salesman Problem, approximation results. The Held-Karp bound. Gomory-Chvátal cuts. Valid inequalities for mixed-integer sets. Superadditive duality, the group problem. Enumeration algorithms.

Textbook: none

Further reading:

G.L. Nemhauser, L.A. Wolsey: Integer and Combinatorial Optimization, John Wiley and Sons, New York, 1999.

D. Bertsimas, R. Weismantel: Optimization over Integers, Dynamic Ideas, Belmont, 2005.

Title of the course: Integer Programming II

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tamás Király

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Sperner systems, binary sets defined by inequalities. Lattices, basis reduction. Integer programming in fixed dimension. The ellipsoid method, equivalence of separation and optimization. The Lift and Project method. Valid inequalities for the Traveling Salesman Problem. LP-based approximation algorithms.

Textbook: none

Further reading:

G.L. Nemhauser, L.A. Wolsey: Integer and Combinatorial Optimization, John Wiley and Sons, New York, 1999.

D. Bertsimas, R. Weismantel: Optimization over Integers, Dynamic Ideas, Belmont, 2005.

Title of the course: Introduction to information theory

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): István Szabó

Department(s): Department of Probability Theory and Statistics

Evaluation: oral or written examination

Prerequisites: Probability theory and Statistics

A short description of the course:

Source coding via variable length codes and block codes. Entropy and its formal properties. Information divergence and its properties. Types and typical sequences. Concept of noisy channel, channel coding theorems. Channel capacity and its computation. Source and channel coding via linear codes. Multi-user communication systems: separate coding of correlated sources, multiple access channels.

Textbook: none

Further reading:

Csiszár – Körner: Information Theory: Coding Theorems for Discrete Memoryless Systems. Akadémiai Kiadó, 1981.

Cover – Thomas: Elements of Information Theory. Wiley, 1991.

Title of the course: Introduction to Topology

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): András Szűcs

Department(s): Department of Analysis

Evaluation: written examination

Prerequisites:

A short description of the course:

Topological spaces and continuous maps. Constructions of spaces: subspaces, quotient spaces, product spaces, functional spaces. Separation axioms, Urison’s lemma. Tietze theorem.Countability axioms., Urison’s metrization theorem. Compactness, compactifications, compact metric spaces. Connectivity, path-connectivity. Fundamental group, covering maps.

The fundamental theorem of Algebra, The hairy ball theorem, Borsuk-Ulam theorem.

Textbook:

Further reading:

J. L. Kelley: General Topology, 1957, Princeton.

Title of the course: Inventory Management

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Gergely Mádi-Nagy

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course: Harris formula (EOQ), Wagner-Whitin model, Silver-Meal heuristics, (R,Q ) and (s,S) policy, The KANBAN system.

Textbook: none

Further reading:

Sven Axäter: Inventory Control, Kluwer, Boston, 2000, ISBN 0-7923-7758-3.

Title of the course: Investments Analysis

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): Róbert Fullér

Department(s): Department of Operations Research

Evaluation: written examination

Prerequisites: none

A short description of the course:

Active portfolio management: The Treynor-Black model. Portfolio performance evaluation. Pension fund performance evaluation. Active portfolio management. Forint-weighted versus time-weighted returns.

Textbook:

Bodie/Kane/Marcus, Investments (Irwin, 1996)

Further reading:

Title of the course: LEMON library: Solving optimization problems in C++

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): Alpár Jüttner

Department(s): Department of Operations Research

Evaluation: Implementing an optimization algorithm.

Prerequisites:

A short description of the course:

LEMON is an open source software library for solving graph and network optimization related algorithmic problems in C++. The aim of this course is to get familiar with the structure and usage of this tool, through solving optimization tasks. The audience also have the opportunity to join to the development of the library itself.

Textbook: none

Further reading:

http://lemon.cs.elte.hu

Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Network Flows. Prentice Hall, 1993.

W.J. Cook, W.H. Cunningham, W. Puleyblank, and A. Schrijver. Combinatorial Optimization. Series in Discrete Matehematics and Optimization. Wiley-Interscience, Dec 1997.

A. Schrijver. Combinatorial Optimization - Polyhedra and Efficiency. Springer-Verlag, Berlin, Series: Algorithms and Combinatorics , Vol. 24, 2003

Title of the course: Lie Groups and Symmetric Spaces

Number of contact hours per week: 4+2

Credit value: 6+3

Course coordinator(s): László Verhóczki

Department(s): Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Lie groups and their Lie algebras. Exponential mapping, adjoint representation, Hausdorff-Baker-Campbell formula. Structure of Lie algebras; nilpotent, solvable, semisimple, and reductive Lie algebras. Cartan subalgebras, classification of semisimple Lie algebras.

Differentiable structure on a coset space. Homogeneous Riemannian spaces. Connected compact Lie groups as symmetric spaces. Lie group formed by isometries of a Riemannian symmetric space. Riemannian symmetric spaces as coset spaces. Constructions from symmetric triples. The exact description of the exponential mapping and the curvature tensor. Totally geodesic submanifolds and Lie triple systems. Rank of a symmetric space. Classification of semisimple Riemannian symmetric spaces. Irreducible symmetric spaces.

Textbook:

S. Helgason: Differential geometry, Lie groups, and symmetric spaces. Academic Press, New York, 1978.

Further reading:

O. Loos: Symmetric spaces I–II. Benjamin, New York, 1969.

Title of the course: Linear Optimization

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tibor Illés

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Goldman-Tucker model. Self-dual linear programming problems, Interior point condition, Goldman-Tucker theorem, Sonnevend theorem, Strong duality, Farkas lemma, Pivot algorithms.

Textbook: none

Further reading:

Katta G. Murty: Linear Programming. John Wiley & Sons, New York, 1983.

Vašek Chvátal: Linear Programming. W. H. Freeman and Company, New York, 1983.

C. Roos, T. Terlaky and J.-Ph. Vial: Theory and Algorithms for Linear Optimization: An Interior Point Approach. John Wiley & Sons, New York, 1997.

Title of the course: Macroeconomics and the Theory of Economic Equilibrium

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Mádi-Nagy Gergely

Department(s): Department of Operations Research

Evaluation: written examination

Prerequisites: none

A short description of the course:

GDP growth factors. Relation between fiscal and monetary policies. Inflation, taxes and interes rates. Consumption versus savings. Money markets and stock markets. Employment and labor market. Exports and imports. Analysis of macroeconomic models.

Textbook:

Paul A. Samuelson-William D. Nordhaus, Economics, Irwin Professiona Publishers, 2004.

Further reading:

McCuerty S.: Macroeconomic Theory, Harper & Row Publ. 1990.

Sargent Th. J.: Macroeconomic Theory, Academic Press, 1987.

Whiteman Ch. H.: Problems in Macroeconomic Theory, Academic Press, 1987.

Title of the course: Manufacturing process management

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tamás Király

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Production as a physical and information process. Connections of production management within an enterprise.

Harris formula, determination of optimal lot size: Wagner-Within model and generalizations,

balancing assembly lines, scheduling of flexible manufacturing systems, team technology, MRP and JIT systems.

Textbook:

Ajánlott irodalom:

Title of the course: Market analysis

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Róbert Fullér

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Description of the current state of some market (e.g. wholesale food markets, electric power markets, the world market of wheat and maize); price elasticities, models using price elasticities, determination of price elasticities from real life data; dynamic models, trajectories in linear and non-linear models; attractor, Ljapunov exponent, fractals, measurement of Ljapunov exponents and fractal dimension using computer.

Textbook:

Further reading:

Title of the course: Markov chains in discrete and continuous time

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): Vilmos Prokaj

Department(s): Department of Probability Theory and Statistics

Evaluation: oral or written examination

Prerequisites: Probability theory and Statistics

A short description of the course:

Markov property and strong Markov property for stochastic processes. Discrete time Markov chains with stationary transition probabilities: definitions, transition probability matrix. Classification of states, periodicity, recurrence. The basic limit theorem for the transition probabilities. Stationary probability distributions. Law of large numbers and central limit theorem for the functionals of positive recurrent irreducible Markov chains. Transition probabilities with taboo states. Regular measures and functions. Doeblin’s ratio limit theorem. Reversed Markov chains.

Absorption probabilities. The algebraic approach to Markov chains with finite state space. Perron-Frobenius theorems.

Textbook: none

Further reading:

Karlin – Taylor: A First Course in Stochastic Processes, Second Edition. Academic Press, 1975

Chung: Markov Chains With Stationary Transition Probabilities. Springer, 1967.

Isaacson – Madsen: Markov Chains: Theory and Applications. Wiley, 1976.

Title of the course: Mathematical Logic

Number of contact hours per week: 2+0 (noncompulsory practice)

Credit value: 2

Course coordinator(s): Péter Komjáth

Department(s): Department of Computer Science

Evaluation: oral examination

Prerequisites:

A short description of the course:

Predicate calculus and first order languages. Truth and satisfiability. Completeness. Prenex norm form. Modal logic, Kripke type models. Model theory: elementary equivalence, elementary submodels. Tarski-Vaught criterion, Löwenheim-Skolem theorem. Ultraproducts.

Gödel’s compactness theorem. Preservation theorems. Beth’s interpolation theorem. Types omitting theorem. Partial recursive and recursive functions. Gödel coding. Church thesis. Theorems of Church and Gödel. Formula expressing the consistency of a formula set. Gödel’s second incompleteness theorem. Axiom systems, completeness, categoricity, axioms of set theory. Undecidable theories.

Textbook:

Further reading:

Title of the course: Mathematics of networks and the WWW

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator: András Benczúr

Department: Department of Computer Science

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Anatomy of search engines. Ranking in search engines. Markov chains and random walks in graphs. The definition of PageRank and reformulation. Personalized PageRank, Simrank.

Kleinberg’s HITS algorithm. Singular value decomposition and spectral graph clustering. Eigenvalues and expanders.

Models for social networks and the WWW link structure. The Barabási model and proof for the degree distribution. Small world models.

Consistent hashing with applications for Web resource cacheing and Ad Hoc mobile routing.

Textbook: none

Further reading:

Searching the Web. A Arasu, J Cho, H Garcia-Molina, A Paepcke, S Raghavan. ACM Transactions on Internet Technology, 2001

Randomized Algorithms, R Motwani, P Raghavan, ACM Computing Surveys, 1996

The PageRank Citation Ranking: Bringing Order to the Web, L. Page, S. Brin, R. Motwani, T. Winograd. Stanford Digital Libraries Working Paper, 1998.

Authoritative sources in a hyperlinked environment, J. Kleinberg. SODA 1998.

Clustering in large graphs and matrices, P Drineas, A Frieze, R Kannan, S Vempala, V Vinay

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms, 1999.

David Karger, Alex Sherman, Andy Berkheimer, Bill Bogstad, Rizwan Dhanidina, Ken Iwamoto, Brian Kim, Luke Matkins, Yoav Yerushalmi: Web Caching and Consistent Hashing, in Proc. WWW8 conference Dept. of Appl. Analysis and Computational Math.

Title of the course: Matroid theory

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): András Frank

Department(s): Department of Operations Research

Evaluation: oral examination

Prerequisites:

Short description of the course:

Matroids and submodular functions. Matroid constructions. Rado's theorem, Edmonds’ matroid intersection theorem, matroid union. Algorithms for intersection and union. Applications in graph theory (disjoint trees, covering with trees, rooted edge-connectivity).

Textbook:

András Frank: Connections in combinatorial optimization (electronic notes).

Further reading:

W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial Optimization, John Wiley and Sons, 1998.

B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms, Springer, 2000.,

E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, 1976.

J. G. Oxley, Matroid Theory, Oxford Science Publication, 2004.,

Recski A., Matriod theory and its applications, Springer (1989).,

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24 of the series Algorithms and Combinatorics.,

D. J.A. Welsh, Matroid Theory, Academic Press, 1976.

Title of the course: Microeconomy

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Gergely Mádi-Nagy

Department(s): Department of Operations Research

Evaluation: written examination

Prerequisites: none

A short description of the course:

The production set, plan and function, The isoquant set, Cobb-Douglas and Leontief technology, Hostelling lemma, The Le Chatelier principle, Cost minimization, The weak axiom of cost minimization, Hicks and Marshall demand function, Hicks and Slutsky compensation, Roy identity, Monetary utility, Engel curve, Giffen effect, Slutsky equation, Properties of demand function, Axioms of observed preferences, Afriat theorem, Approximation of preference relation in GARP model, Product aggregation, Hicks separability, Functional separability, Consumer aggregation, Perfect competitive market, Supply in competitive markets, Optimal production quantity, Inverse supply function, Pareto optimality, Market entering, Representative manufacturer and consumer, Several manufacturers and consumers, Oligopoly and monopoly markets, Welfare economics.

Textbook: Hal R. Varian, Microeconomic Analysis, Norton, New York, 1992.

Further reading:

M. L. Montgomery, Topics in Multiplicative Number Theory, Springer, Berlin-Heidelberg-New York, 1971. (Lecture Notes in Mathematics 227)

Title of the course: Multivariate statistical methods

Number of contact hours per week: 4+0

Credit value: 4

Course coordinator(s): György Michaletzky

Department(s): Department of Probability Theory and Statistics

Evaluation: oral or written examination

Prerequisites: Probability Theory and Statistics

A short description of the course:

Estimation of the parameters of multidimensional normal distribution. Matrix valued distributions. Wishart distribution: density function, determinant, expected value of its inverse.

Hypothesis testing for the parameters of multivariate normal distribution. Independence, goodness-of-fit test for normality. Linear regression.

Correlation, maximal correlation, partial correlation, kanonical correlation.

Principal component analysis, factor analysis, analysis of variances.

Contingency tables, maximum likelihood estimation in loglinear models. Kullback–Leibler divergence. Linear and exponential families of distributions. Numerical method for determining the L-projection (Csiszár’s method, Darroch–Ratcliff method)

Textbook: none

Further reading:

J. D. Jobson, Applied Multivariate Data Analysis, Vol. I-II. Springer Verlag, 1991, 1992.

C. R. Rao: Linear statistical inference and its applications, Wiley and Sons, 1968,

Title of the course: Nonlinear functional analysis and its applications

Number of contact hours per week: 3+2

Credit value: 4+3

Course coordinator(s): János Karátson

Department(s): Dept. of Appl. Analysis and Computational Math.

Evaluation: oral examination and home exercises

Prerequisites:

A short description of the course:

Basic properties of nonlinear operators. Derivatives, potential operators, monotone operators, duality.

Solvability of operator equations. Variational principle, minimization of functionals.

Fixed point theorems. Applications to nonlinear differential equations.

Approximation methods in Hilbert space. Gradient type and Newton-Kantorovich iterative solution methods. Ritz–Galjorkin type projection methods.

Textbook: none

Further reading: Zeidler, E.: Nonlinear functional analysis and its applications I-III. Kantorovich, L.V., Akilov, G.P.: Functional Analysis

Title of the course: Nonlinear Optimization

Number of contact hours per week: 3+0

Credit value: 4

Course coordinator(s): Tibor Illés

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course: Convex sets, convex functions, convex inequalities. Extremal points, extremal sets. Krein-Milman theorem. Convex cones. Recession direction, recession cones. Strictly-, strongly convex functions. Locally convex functions. Local minima of the functions. Characterization of local minimas. Stationary points. Nonlinear programming problem. Characterization of optimal solutions. Feasible, tangent and decreasing directions and their forms for differentiable and subdifferentiable functions. Convex optimization problems. Separation of convex sets. Separation theorems and their consequences. Convex Farkas theorem and its consequences. Saddle-point, Lagrangean-function, Lagrange multipliers. Theorem of Lagrange multipliers. Saddle-point theorem. Necessary and sufficient optimality conditions for convex programming. Karush-Kuhn-Tucker stationary problem. Karush-Kuhn-Tucker theorem. Lagrange-dual problem. Weak and strong duality theorems. Theorem of Dubovickij and Miljutin. Specially structured convex optimization problems: quadratic programming problem. Special, symmetric form of linearly constrained, convex quadratic programming problem. Properties of the problem. Weak and strong duality theorem. Equivalence between the linearly constrained, convex quadratic programming problem and the bisymmetric, linear complementarity problem. Solution algorithms: criss-cross algorithm, logarithmic barrier interior point method.

Textbook: none

Further reading:

Béla Martos: Nonlinear Programming: Theory and Methods. Akadémiai Kiadó, Budapest, 1975.

M. S. Bazaraa, H. D. Sherali and C. M. Shetty: Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, New York, 1993.

J.-B. Hiriart-Urruty and C. Lemaréchal: Convex Analysis and Minimization Algorithms I-II. Springer-Verlag, Berlin, 1993.

J. P. Aubin: Mathematical Methods of Game and Economic Theor. North-Holland, Amsterdam, 1982.

D. P. Bertsekas: Nonlinear Programming. Athena Scientific, 2004.

Title of the course: Number theory 2.

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): András Sárközy

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Elements of multiplicative number theory. Dirichlet's theorem,special cases. Elements of combinatorial number theory. Diophantine equations. The two square problem. Gaussian integers, special quadraticextensions. Special cases of Fermat's last theorem. The four squareproblem, Waring's problem. Pell equations. Diophantine approximation theory. Algebraic and transcendent numbers. The circle problem, elements of the geometry of numbers. The generating function method, applications. Estimates involving primes. Elements of probabilistic number theory.

Textbook: none

Further reading:

I. Niven, H.S. Zuckerman: An introduction to the theory of Numbers. Wiley, 1972.

Title of the course: Operations Research Project

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): Róbert Fullér

Department(s): Department of Operations Research

Evaluation: written examination

Prerequisites: none

A short description of the course:

We model real life problems with operational research methods.

Topics: Portfolio optimization models, Decision support systems, Project management models, Electronic commerce, Operations research models in telecommunication, Heuristic yield management

Textbook: Paul A. Jensen and Jonathan F. Bard, Operations Research Models and Methods (John

Wiley and Sons, 2003)

Further reading: Mahmut Parlar, Interactive Operations Research with Maple: Methods and

Models (Birkhauser, Boston, 2000)

Title of the course: Operator semigroups

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): András Bátkai

Department(s): Dept. of Appl. Analysis and Computational math.

Evaluation: oral or written examination and course work

Prerequisites:

A short description of the course:

Linear theory of operator semigroups. Abstract linear Cauchy problems, Hille-Yosida theory. Bounded and unbounded perturbation of generators. Spectral theory for semigroups and generators. Stability and hyperbolicity of semigroups. Further asymptotic properties.

Textbook: Engel, K.-J. and Nagel, R.: One-parameter Semigroups for Linear Evolution Equations, Springer, 2000.

Further reading:

Title of the course: Partial differential equations

Number of contact hours per week: 4+2

Credit value: 6+3

Course coordinator(s): László Simon

Department(s): Dept. of Appl. Analysis and Computational math.

Evaluation: oral examination and tutorial mark

Prerequisites:

A short description of the course:

Fourier transform. Sobolev spaces. Weak, variational and classical solutions of boundary value problems for linear elliptic equations (stationary heat equation, diffusion). Initial-boundary value problems for linear equations (heat equation, wave equation): weak and classical solutions by using Fourier method and Galerkin method.

Weak solutions of boundary value problems for quasilinear elliptic equations of divergence form, by using the theory of monotone and pseudomonotone operators. Elliptic variational inequalities. Quasilinear parabolic equations by using the theory of monotone type operators. Qualitative properties of the solutions. Quasilinear hyperbolic equations.

Textbook: none

Further reading:

R.E. Showalter: Hilbert Space Method for Partial Differential Equations, Pitman, 1979;

E. Zeidler: Nonlinear Functional Analysis and its Applications II, III, Springer, 1990.

Title of the course: Polyhedral combinatorics

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tamás Király

Department(s): Department of Operations Research

Evaluation: oral examination and tutorial mark

Prerequisites:

A short description of the course:

Total dual integrality. Convex hull of matchings. Polymatroid intersection theorem, submodular flows and their applications in graph optimization (Lucchesi-Younger theorem, Nash-Williams’ oritentation theorem).

Textbook:

Further reading:

W.J. Cook, W.H. Cunningham, W.R. Pulleybank, and A. Schrijver, Combinatorial Optimization, John Wiley and Sons, 1998.

B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms, Springer, 2000.

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24 of the series Algorithms and Combinatorics.

Title of the course: Probability and Statistics

Number of contact hours per week: 3+2

Credit value: 3+3

Course coordinator(s): Tamás F. Móri

Department(s): Department of Probability Theory and Statistics

Evaluation: oral or written examination and tutorial mark

Prerequisites: -

A short description of the course:

Probability space, random variables, distribution function, density function, expectation, variance, covariance, independence.

Types of convergence: a.s., in probability, in L_p, weak. Uniform integrability.

Characteristic function, central limit theorems.

Conditional expectation, conditional probability, regular version of conditional distribution, conditional density function.

Martingales, submartingales, limit theorem, regular martingales.

Strong law of large numbers, series of independent random variables, the 3 series theorem.

Statistical field, sufficiency, completeness.

Fisher information. Informational inequality. Blackwell-Rao theorem. Point estimation: method of moments, maximum likelihood, Bayes estimators.

Hypothesis testing, the likelihood ratio test, asymptotic properties.

The multivariate normal distribution, ML estimation of the parameters

Linear model, least squares estimator. Testing linear hypotheses in Gaussian linear models.

Textbook: none

Further reading:

J. Galambos: Advanced Probability Theory. Marcel Dekker, New York, 1995.

E. L. Lehmann: Theory of Point Estimation. Wiley, New York, 1983.

E. L. Lehmann: Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986.

Title of the course: Reading course in Analysis

Number of contact hours per week: 0+2

Credit value: 5

Course coordinator(s): Tóth Árpád

Department(s): Department of Analysis

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Real functions. Functions of bounded variation. Riemann-Stieltjes integral, line integrals. The inverse and implicit function theorems. Optimum problems with constraints. Measure theory. The Lebesgue integral. Function spaces. Complex analysis. Cauchy's theorem and integral formula. Power series expansion of analytic functions. Isolated singular points, the residue theorem. Ordinary differential equations. Theorems on existence and uniqueness. Elementary methods. Linear equations and systems. Hilbert spaces, orthonormal systems. Metric spaces, basic topological concepts, sequences, limits and continuity of functions. Numerical methods.

Textbook: none

Further reading:

W. Rudin: Principles of mathematical analyis,

W. Rudin: Real and complex analyis,

F. Riesz and B. Szokefalvi-Nagy: Functional analysis.

G. Birkhoff and G-C. Rota: Ordinary Differential Equations,

J. Munkres: Topology.

Title of the course: Representations of Banach-*-algebras and Abstract Harmonic Analysis

Number of contact hours per week: 2+1

Credit value: 2+2

Course coordinator(s): János Kristóf

Department(s): Dept. of Appl. Analysis and Computational math.

Evaluation: oral and written examination

Prerequisites:

A short description of the course:

Representations of *-algebras. Positive functionals and GNS-construction. Representations of Banach-*-algebras. Gelfand-Raikoff theorem. The second Gelfand-Naimark theorem. Hilbert-integral of representations. Spectral theorems for C*-algebras and measurable functional calculus. Basic properties of topological groups. Continuous topological and unitary representations. Radon measures on locally compact spaces. Existence and uniqueness of left Haar-measure on locally compact groups. The modular function of a locally compact group. Regular representations. The group algebra of a locally compact group. The main theorem of abstract harmonic analysis. Gelfand-Raikoff theorem. Unitary representations of compact groups (Peter-Weyl theorems). Unitary representations of commutative locally compact groups (Stone-theorems). Factorization of Radon measures. Induced unitary representations (Mackey-theorems).

Textbook:

Further reading:

J. Dixmier: Les C*-algébres et leurs représentations, Gauthier-Villars Éd., Paris, 1969

E.Hewitt-K.Ross: Abstract Harmonic Analysis, Vols I-II, Springer-Verlag, 1963-1970

Title of the course: Riemann surfaces

Number of contact hours per week: 2+0,

Credit value: 3

Course coordinator(s): Róbert Szőke

Department(s): Department of Analysis

Evaluation: oral or written examination

Prerequisites: Complex analysis (Bsc),

Algebraic topology (Bsc),

Algebra IV (Bsc)

A short description of the course:

Abstract definition, coverings, analytic continuation, homotopy, theorem of monodromy, universal covering, covering group, Dirichlet's problem, Perron's method, Green function, homology, residue theorem, uniformization theorem for simply connected Riemann surfaces.

Determining the Riemann surface from its covering group. Fundamental domain, fundamental polygon. Riemann surface of an analytic function, compact Riemann surfaces and complex algebraic curves.

Textbook:

Further reading:

O. Forster: Lectures on Riemann surfaces, GTM81, Springer-Verlag, 1981

Title of the course: Riemannian Geometry

Number of contact hours per week: 4+2

Credit value: 6+3

Course coordinator(s): Balázs Csikós

Department(s): Department of Geometry

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

The exponential mapping of a Riemannian manifold. Variational formulae for the arc length. Conjugate points. The index form assigned to a geodesic curve. Completeness of a Riemannian manifold, the Hopf-Rinow theorem. Rauch comparison theorems. Non-positively curved Riemannian manifolds, the Cartan-Hadamard theorem. Local isometries between Riemannian manifolds, the Cartan-Ambrose-Hicks theorem. Locally symmetric Riemannian spaces.

Submanifold theory: Connection induced on a submanifold. Second fundamental form, the Weingarten equation. Totally geodesic submanifolds. Variation of the volume, minimal submanifolds. Relations between the curvature tensors. Fermi coordinates around a submanifold. Focal points of a submanifold.

Textbooks:

1. M. P. do Carmo: Riemannian geometry. Birkhäuser, Boston, 1992.

2. J. Cheeger, D. Ebin: Comparison theorems in Riemannian geometry. North-Holland,
Amsterdam 1975.

Further reading:

S. Gallot, D. Hulin, J. Lafontaine: Riemannian geometry. Springer-Verlag, Berlin, 1987.

Title of the course: Rings and algebras

Number of contact hours per week: 2+2

Credit value: 2+3

Course coordinator(s): István Ágoston

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Asociative rings and algebras. Constructions: polynomials, formal power series, linear operators, group algebras, free algebras, tensor algebras, exterior algebras. Structure theory: the radical, direct and semidirect decompositions. Chain conditions. The Hilbert Basis Theorem, the Hopkins theorem.

Categories and functors. Algebraic and topological examples. Natural transformations. The concept of categorical equivalence. Covariant and contravariant functors. Properties of the Hom and tensor functors (for non-commutative rings). Adjoint functors. Additive categories, exact functors. The exactness of certain functors: projective, injective and flat modules.

Homolgical algebra. Chain complexes, homology groups, chain homotopy. Examples from algebra and topology. The long exact sequence of homologies.

Commutative rings. Ideal decompositions. Prime and primary ideals. The prime spectrum of a ring. The Nullstellensatz of Hilbert.

Lie algebras. Basic notions, examples, linear Lie algebras. Solvable and nilpotent Lie algebras. Engel’s theorem. Killing form. The Cartan subalgebra. Root systems and quadratic forms. Dynkin diagrams, the classification of semisimple complex Lie algebras. Universal enveloping algebra, the Poincaré–Birkhoff–Witt theorem.

Textbook: none

Further reading:

Cohn, P.M.: Algebra I-III. Hermann, 1970, Wiley 1989, 1990.

Jacobson, N.: Basic Algebra I-II. Freeman, 1985, 1989.

Humphreys, J.E.: Introduction to Lie algebras and representation theory. Springer, 1980.

Title of the course: Scheduling theory

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tibor Jordán

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Classification of scheduling problems; one-machine scheduling, priority rules (SPT, EDD, LCL), Hodgson algorithm, dynamic programming, approximation algorithms, LP relaxations. Parallel machines, list scheduling, LPT rule, Hu's algorithm. Precedence constraints, preemption. Application of network flows and matchings. Shop models, Johnson's algorithm, timetables, branch and bound, bin packing.

Textbook: T. Jordán, Scheduling, lecture notes.

Further reading:

Title of the course: Selected topics in graph theory

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): László Lovász

Department(s): Department of Computer Science

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Selected topics in graph theory. Some topics: eigenvalues, automorphisms, graph polynomials (e.g., Tutte polynomial), topological problems

Textbook: none

Further reading:

L. Lovász: Combinatorial Problems and Exercises, AMS, Providence, RI, 2007.

Title of the course: Seminar in complex analysis

Number of contact hours per week: 0+2

Credit value: 2

Course coordinator(s): Róbert Szőke

Department(s): Department of Analysis

Evaluation: oral or written examination or lecture on a selected topic

Prerequisites: Topics in complex analysis (MSc)

A short description of the course:

There is no fixed syllabus. Covering topics (individual or several papers on a particular subject) related to the first semester “Topics in complex analysis”

course, mostly by the lectures of the participating students.

Textbook: none

Further reading:

Title of the course: Set Theory (introductory)

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator(s): Péter Komjáth

Department(s): Department of Computer Science

Evaluation: oral examination

Prerequisites:

A short description of the course:

Naive and axiomatic set theory. Subset, union, intersection, power set. Pair, ordered pair, Cartesian product, function. Cardinals, their comparison. Equivalence theorem. Operations with sets and cardinals. Identities, monotonicity. Cantor’s theorem. Russell’s paradox. Examples. Ordered sets, order types. Well ordered sets, ordinals. Examples. Segments. Ordinal comparison. Axiom of replacement. Successor, limit ordinals. Theorems on transfinite induction, recursion. Well ordering theorem. Trichotomy of cardinal comparison. Hamel basis, applications. Zorn lemma, Kuratowski lemma, Teichmüller-Tukey lemma. Alephs, collapse of cardinal arithmetic. Cofinality. Hausdorff’s theorem. Kőnig inequality. Properties of the power function. Axiom of foundation, the cumulative hierarchy. Stationary set, Fodor’s theorem. Ramsey’s theorem, generalizations. The theorem of de Bruijn and Erdős. Delta systems.

Textbook:

A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.

Further reading:

Title of the course: Set Theory I

Number of contact hours per week: 4+0

Credit value: 6

Course coordinator(s): Péter Komjáth

Department(s): Department of Computer Science

Evaluation: oral examination

Prerequisites:

A short description of the course:

Cofinality, Haussdorff’s theorem. Regular, singular cardinals. Stationary sets. Fodor’s theorem. Ulam matrix. Partition relations. Theorems of Dushnik-Erdős-Miller, Erdős-Rado. Delta systems. Set mappings. Theorems of Fodor and Hajnal. Todorcevic’s theorem. Borel, analytic, coanalytic, projective sets. Regularity properties. Theorems on separation, reduction. The hierarchy theorem. Mostowski collapse. Notions of forcing. Names. Dense sets. Generic filter. The generic model. Forcing. Cohen’s result.

Textbook:

A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.

Further reading:

Title of the course: Set Theory II

Number of contact hours per week: 4+0

Credit value: 6

Course coordinator(s): Péter Komjáth

Department(s): Department of Computer Science

Evaluation: oral examination

Prerequisites:

A short description of the course:

Constructibility. Product forcing. Iterated forcing. Lévy collapse. Kurepa tree. The consistency of Martin’s axiom. Prikry forcing. Measurable, strongly compact, supercompact cardinals. Laver diamond. Extenders. Strong, superstrong, Woodin cardinals. The singular cardinals problem. Saturated ideals. Huge cardinals. Chang’s conjecture. Pcf theory. Shelah’s theorem.

Textbook:

A. Hajnal, P. Hamburger: Set Theory. Cambridge University Press, 1999.

Further reading:

K. Kunen: Set Theory.

A. Kanamori: The Higher Infinite.

Title of the course: Special Functions

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Gábor Halász

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: Complex Functions (BSc),

Fourier Integral (BSc)

A short description of the course:

Gamma function. Stirling formula in the complex plane, saddle point method.

Zeta function. Functional equation, elementary facts about zeros. Prime number theorem.

Elliptic functions. Parametrization of elliptic curves, lattices. Fundamental domain for the anharmonic and modular group.

Functional equation for the theta function. Holomorphic modular forms. Their application to the four square theorem.

Textbook:

Further reading:

E.T. Whittaker and G.N. Watson: A Course of Modern Analysis, University Press, Cambridge, 1927.

E.C. Titchmarsh (and D.R. Heath-Brown: The Theory of the Riemann Zeta-function, Oxford University Press, 1986.

C.L. Siegel: Topics in Complex Function Theory, John Wiley & Sons, New York, 1988, volume I.

R.C. Gunning: Lectures on Modular Forms, Princeton University Press, 1962, 96 pages

Title of the course: Statistical computing 1

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): Zempléni András

Department(s): Department of Probability and Statistics

Evaluation: weekly homework or final practical and written examination, tutorial mark

Prerequisites: Probability and statistics

A short description of the course:

Statistical hypothesis testing and parameter estimation: algorithmic aspects and technical instruments. Numerical-graphical methods of descriptive statistics. Estimation of the location and scale parameters. Testing statistical hypotheses. Probability distributions.

Representation of distribution functions, random variate generation, estimation and fitting probability distributions. The analysis of dependence. Analysis of variance. Linear regression models. A short introduction to statistical programs of different category: instruments for demonstration and education, office environments, limited tools of several problems, closed programs, expert systems for users and specialists.

Computer practice (EXCEL, Statistica, SPSS, SAS, R-project).

Textbook:

Further reading:

http://office.microsoft.com/en-us/excel/HP100908421033.aspx

http://www.statsoft.com/textbook/stathome.html

http://www.spss.com/stores/1/Training_Guides_C10.cfm

http://support.sas.com/documentation/onlinedoc/91pdf/sasdoc_91/insight_ug_9984.pdf

http://www.r-project.org/doc/bib/R-books.html

http://www.mathworks.com/access/helpdesk/help/pdf_doc/stats/stats.pdf

Title of the course: Statistical computing 2

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): Zempléni András

Department(s): Department of Probability and Statistics

Evaluation: weekly homework or final practical and written examination, tutorial mark

Prerequisites: Multidimensional statistics

A short description of the course:

Multidimensional statistics: review of methods and demonstration of computer instruments.

Dimension reduction. Principal components, factor analysis, canonical correlation. Multivariate Analysis of Categorical Data. Modelling binary data, linear-logistic model.

Principle of multidimensional scaling, family of deduced methods. Correspondence analysis. Grouping. Cluster analysis and classification. Statistical methods for survival data analysis.

Probit, logit and nonlinear regression. Life tables, Cox-regression.

Computer practice. Instruments: EXCEL, Statistica, SPSS, SAS, R-project.

Textbook:

Further reading:

http://www.statsoft.com/textbook/stathome.html

http://www.spss.com/stores/1/Training_Guides_C10.cfm

http://support.sas.com/documentation/onlinedoc/91pdf/sasdoc_91/stat_ug_7313.pdf

http://www.r-project.org/doc/bib/R-books.html

http://www.mathworks.com/access/helpdesk/help/pdf_doc/stats/stats.pdf

Title of the course: Statistical hypothesis testing

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Villő Csiszár

Department(s): Department of Probability Theory and Statistics

Evaluation: oral examination

Prerequisites: Probability and statistics

A short description of the course:

Monotone likelihood ratio, testing hypotheses with one-sided alternative. Testing with two-sided alternatives in exponential families. Similar tests, Neyman structure. Hypothesis testing in presence of nuisance parameters.

Optimality of classical parametric tests. Asymptotic tests. The generalized likelihood ratio test. Chi-square tests.

Convergence of the empirical process to the Brownian bridge. Karhunen-Loève expansion of Gaussian processes. Asymptotic analysis of classical nonparametric tests.

Invariant and Bayes tests.

Connection between confidence sets and hypothesis testing.

Textbook: none

Further reading:

E. L. Lehmann: Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986.

Title of the course: Stochastic optimization

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Csaba Fábián

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Static and dynamic models.

Mathematical characterization of stochastic programming problems. Solution methods.

Theory of logconcave measures. Logconcavity of probabilistic constraints. Estimation of constraint functions through simulation.

Textbook:

Further reading:

Kall, P., Wallace, S.W., Stochastic Programming, Wiley, 1994.

Prékopa A., Stochastic Programming, Kluwer, 1995.

Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, Springer, 1997-1999.

Title of the course: Stochastic optimization practice

Number of contact hours per week: 0+2

Credit value: 3

Course coordinator(s): Csaba Fábián

Department(s): Department of Operations Research

Evaluation: tutorial mark

Prerequisites:

A short description of the course:

Examples of stochastic models. Different formulations of aims and constraints: by expectations or probabilities.

Building simple models, formulating and solving the deriving mathematical programming problems. Applications.

Textbook:

Further reading:

Kall, P., Wallace, S.W., Stochastic Programming, Wiley, 1994.

Prékopa A., Stochastic Programming, Kluwer, 1995.

Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, Springer, 1997-1999.

Title of the course: Stochastic processes with independent increments, limit theorems

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Vilmos Prokaj

Department(s): Department of Probability Theory and Statistics

Evaluation: oral or written examination

Prerequisites: Probability theory and Statistics

A short description of the course:

Infinitely divisible distributions, characteristic functions. Poisson process, compound Poisson-process. Poisson point-process with general characteristic measure. Integrals of point-processes. Lévy–Khinchin formula. Characteristic functions of non-negative infinitely divisible distributions with finite second moments. Characteristic functions of stable distributions.

Limit theorems of random variables in triangular arrays.

Textbook: none

Further reading:

Y. S. Chow – H. Teicher: Probability Theory: Independence, Interchangeability, Martingales. Springer, New York, 1978.

W. Feller: An Introduction to Probability Theory and its Applications, vol. 2. Wiley, New York, 1966.

Title of the course: Structures in combinatorial optimization

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Tibor Jordán

Department(s): Department of Operations Research

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Chains and antichains in partially ordered sets, theorems of Greene and Kleitman.

Mader's edge splitting theorem. The strong orientation theorem of Nash-Williams.

The interval generator theorem of Győri.

Textbook:

A. Frank, Structures in combinatorial optimization, lecture notes

Further reading:

A. Schrijver, Combinatorial Optimization: Polyhedra and efficiency, Springer, 2003. Vol. 24 of the series Algorithms and Combinatorics.

Title of the course: Supplementary chapters of topology I. – Topology of singularities. (special material)

Number of contact hours per week: 2+0

Credit value: 3

Lecturer: András Némethi (scientific advisor, Rényi Institut)

Course coordinator(s): András Szűcs (professor)

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: BSc Algebraic Topology material

A short description of the course:

1) Complex algebraic curves

2) holomorphic functions of many variables

3) implicit function theorem

4) smooth and singular analytic varieties

5) local singularities of plane curves

6) Newton diagram, Puiseux theorem

7) Resolution of plane curve singularities

8) Resolution graphs

9) topology of singularities, algebraic knots

10) Milnor fibration

11) Alexander polynomial, monodromy, Seifert matrix

12) Projective plane curves

13) Dual curve, Plucker formulae

14) Genus, Hurwitz-, Clebsh, Noether formulae

15) Holomorphic differential forms

16) Abel theorem

Textbook:

Further reading:

C. T. C. Wall: singular points of plane curves, London Math. Soc. Student Texts 63.

F. Kirwan: Complex Algebraic Curves, London Math. Soc. Student Texts 23.

E. Brieskorn, H. Korner: Plane Algebraic Curves, Birkhauser

Title of the course: Supplementary Chapters of Topology II Low dimensional manifolds

Number of contact hours per week: 2+0

Credit value: 3

Lecturer: András Stipsicz (scientific advisor, Rényi Institut)

Course coordinator(s): András Szűcs (professor)

Department(s): Department of Analysis

Evaluation: oral examination

Prerequisites: BSc Algebraic Topology

A short description of the course:

1) handle-body decomposition of manifolds

2) knots in 3-manfolds, their Alexander polynomials

3) Jones polynomial, applications

4) surfaces and mapping class groups

5) 3-manifolds, examples

6) Heegard decomposition and Heegard diagram

7) 4-manifolds, Freedman and Donaldson theorems (formulations)

8) Lefschetz fibrations

9) invariants (Seiberg-Witten and Heegard Floer invariants),

10) applications

Textbook:

Further reading:

J. Milnor: Morse theory

R.E. Gompf, A. I. Stipsicz: 4-manifolds and Kirby calculus, Graduate Studies in Mathematics, Volume 20, Amer. Math. Soc. Providence, Rhode Island.

Title of the course: Topics in Analysis

Number of contact hours per week: 2+1

Credit value: 2+2

Course coordinator(s): Tamás Keleti

Department(s): Department of Analysis

Evaluation: oral or written examination and tutorial mark

Prerequisites: Analysis IV

A short description of the course:

Hausdorff measure and Hausdorff dimension. The Hausdorff dimension of Rⁿ and some fractals, length and 1-dimensional measure.

Haar measure. Existence and uniqueness.

Approximation theory. Approximation with Fejér means, de la Vallée Poussin operator, Fejér-Hermite interpolation, Bernstein polynom.

The order of approximation. Approximation with analytic functions.

Approximation with polynomials. Tschebishev polynomials.

Textbook: none

Further reading:

P. Halmos: Measure Theory, Van Nostrand, 1950

K.J. Falconer: The Geometry of Fractal Sets, CUP, 1985

D. Jackson: The theory of approximation, AMS, 1994.

Title of the course: Topics in Differential Geometry

Number of contact hours per week: 2+0

Credit value: 2

Course coordinator: Balázs Csikós (associate professor)

Department: Department of Geometry

Evaluation: oral or written examination

Prerequisites:

A short description of the course:

Differential geometric characterization of convex surfaces. Steiner-Minkowski formula, Herglotz integral formula, rigidity theorems for convex surfaces.

Ruled surfaces and line congruences.

Surfaces of constant curvature. Tchebycheff lattices, Sine-Gordon equation, Bäcklund transformation, Hilbert’s theorem. Comparison theorems.

Variational problems in differential geometry. Euler-Lagrange equation, brachistochron problem, geodesics, Jacobi fields, Lagrangian mechanics, symmetries and invariants, minimal surfaces, conformal parameterization, harmonic mappings.

Textbook: none

Further reading:

1. W. Blaschke: Einführung in die Differentialgeometrie. Springer-Verlag, 1950.

2. J. A. Thorpe: Elementary Topics in Differential Geometry. Springer-Verlag, 1979.

3. J. J. Stoker: Differential Geometry. John Wiley & Sons Canada, Ltd.; 1989.

4. F. W. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer-Verlag,
1983.

Title of the course: Topics in group theory

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): Péter P. Pálfy

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination and tutorial mark

Prerequisites: Groups and representations

A short description of the course:

Permutation groups. Multiply transitive groups, Mathieu groups. Primitive permutation groups, the O’Nan-Scott Theorem.

Simple groups. Classical groups, groups of Lie type, sporadic groups.

Group extensions. Projective representations, the Schur multiplier.

p-groups. The Frattini subgroup. Special and extraspecial p-groups. Groups of maximal class.

Subgroup lattices. Theorems of Ore and Iwasawa.

Textbook: none

Further reading:

D.J.S. Robinson: A course in the theory of groups, Springer, 1993

P.J. Cameron: Permutation groups, Cambridge University Press, 1999

B. Huppert, Endliche Gruppen I, Springer, 1967

Title of the course: Topics in ring theory

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): István Ágoston

Department(s): Department of Algebra and Number Theory

Evaluation: oral or written examination and tutorial mark

Prerequisites: Rings and algebras

A short description of the course:

Structure theory: primitive rings, Jacobson’s Density Theorem, the Jacobson radical of a ring, commutativity theorem. Central simple algebras: tensor product of algebras, the Noether–Scolem Theorem, the Double Centralizer Therem, Brauer group, crossed product. Polynomial identities: structure theorems, Kaplansky’s theorem, the Kurosh Problem, combinatorial results, quantitative theory. Noetherian rings: Goldie’s theorems and generalizations, dimension theory. Artinina rings and generalizations: Bass’s characterization of semiperfect and perfect rings, coherent rings, von Neumann regular rings, homological properties. Morita theory: Morita equivalence, Morita duality, Morita invariance. Quasi-Frobenius rings: group algebras, symmetric algebras, homological properties. Representation theory: hereditary algebras, Coxeter transformations and Coxeter functors, preprojective, regular and preinjective representations, almost split sequences, the Baruer–Thrall Conjectures, finite representation type.

The Hom and tensor functors: projective, imjective and flat modules. Derived functors: projective and injective resolutions, the construction and basic properties of the Ext and Tor functors. Exact seuqences and the Ext functor, the Yoneda composition, Ext algebras. Homological dimensions: projective, injective and global dimension, The Hilbert Syzygy Theorem, dominant dimension, finitistic dimension, the finitistic dimension conjecture. Homological methods in representation theory: almost split sequences, Auslander–Reiten quivers. Derived categories: triangulated categories, homotopy category of complexes, localization of categories, the derived category of an algebra, the Morita theory of derived categories by Rickard.

Textbook: none

Further reading:

Anderson, F.–Fuller, K.: Rings and categories of modules, Springer, 1974, 1995

Auslander, M.–Reiten, I.–Smalø: Representation theory of Artin algebras, Cambridge University Press, 1995

Drozd, Yu. –Kirichenko, V.: Finite dimensional algebras, Springer, 1993

Happel, D.: Triangulated categories in the representation theory of finite dimensional algebras, CUP, 1988

Herstein, I.: Noncommutative rings. MAA, 1968.

Rotman, J.: An introduction to homological algebra, AP, 1979

Title of the course: Topological Vector Spaces and Banach-algebras

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator(s): János Kristóf

Department: Dept. of Appl. Analysis and Computational Math.

Evaluation: oral and written examination

Prerequisites:

A short description of the course:

Basic properties of linear topologies. Initial linear topologies. Locally compact topological vector spaces. Metrisable topological vector spaces. Locally convex and polinormed spaces. Inductive limit of locally convex spaces. Krein-Milmans theorem. Geometric form of Hahn-Banach theorem and separation theorems. Bounded sets in topological vector spaces. Locally convex function spaces. Ascoli theorems. Alaoglu-Bourbaki theorem. Banach-Alaoglu theorem. Banach-Steinhaus theorem. Elementary duality theory. Locally convex topologies compatible with duality. Mackey-Arens theorem. Barrelled, bornologic, reflexive and Montel-spaces. Spectrum in a Banach-algbera. Gelfand-representation of a commutative complex Banach-algebra. Banach-*-algebras and C*-algebras. Commutative C*-algebras (I. Gelgand-Naimark theorem). Continuous functional calculus. Universal covering C*-algebra and abstract Stone’s theorem. Positive elements in C*-algebras. Baer C*-algebras.

Compulsory:

Further reading:

N. Bourbaki: Espaces vectoriels topologiques, Springer, Berlin-Heidelberg-New York, 2007

N. Bourbaki: Théories spectrales, Hermann, Paris, 1967

J. Dixmier: Les C*-algébres et leurs représentations, Gauthier-Villars Éd., Paris, 1969

Title of the course: Unbounded operators of Hilbert spaces

Number of contact hours per week: 2+0

Credit value: 3

Course coordinator(s): Sebestyén Zoltán

Department: Dept. of Appl. Analysis and Computational Math.

Evaluation: oral examination

Prerequisites: Functional analysis (BSc)

A short description of the course:

Neumann’s theory of closed Hilbert space operators: existence of the second adjoint and the product of the first two adjoints as a positive selfadjoint operator. Up to date theory of positive selfadjoint extensions of not necessarily densely defined operators on Hilbert space: Krein’s theory revisited. Extremal extensions are characterized including Friedrichs and Krein-von Neumann extensions. Description of a general positive selfadjoint extension.

Textbook:

Further reading:

Title of the course: Universal algebra and lattice theory

Number of contact hours per week: 2+2

Credit value: 3+3

Course coordinator: Emil Kiss

Department: Department of Algebra and Number Theory

Evaluation: oral or written examination and tutorial mark

Prerequisites:

A short description of the course:

Similarity type, algebra, clones, terms, polynomials. Subalgebra, direct product, homomorphism, identity, variety, free algebra, Birkhoff’s theorems. Subalgebra lattices, congruence lattices, Grätzer-Schmidt theorem. Mal’tsev-lemma. Subdirect decomposition, subdirectly irreducible algebras, Quackenbush-problem.

Mal’tsev-conditions, the characterization of congruence permutable, congruence distributive and congruence modular varieties. Jónsson’s lemma, Fleischer-theorem. Congruences of lattices, lattice varieties.

Partition lattices, every lattice is embeddable into a partition lattice. Free lattices, Whitman-condition, canonical form, atoms, the free lattice is semidistributive, the operations are continuous. There exists a fixed point free monotone map.

Closure systems. Complete, algebraic and geometric lattices. Modular lattices. The free modular lattice generated by three elements. Jordan-Dedekind chain condition. Semimodular lattices. Distributive lattices.

Lattices and geometry: subspace lattices of projective geometries. Desargues-identity, geomodular lattices. Coordinatization. Complemented lattices. The congruences of relatively complemented lattices.

The question of completeness, primal and functionally complete algebras, characterizations, discriminator varieties. Directly representable varieties.

The Freese-Lampe-Taylor theorem about the congruence lattice of algebras with a few operations. Abelian algebras, centrality, the properties of the commutator in modular varieties. Difference term, the fundamental theorem of Abelian algebras. Generalized Jónsson-theorem. The characterization of finitely generated, residually small varieties by Freese and McKenzie.

Congruence lattices of finite algebras: the results of McKenzie, Pálfy and Pudlak. Induced algebra, their geometry, relationship with the congruence lattice of the entire algebra. The structure of minimal algebras. Types, the labeling of the congruence lattice. Solvable algebras.

The behavior of free spectrum. Abelian varieties. The distribution of subdirectly irreducible algebras. Finite basis theorems. First order decidable varieties, undecidable problems.

Textbook: none

Further reading:

Burris-Sankappanavar: A course in universal algebra. Springer, 1981.

Freese-McKenzie: Commutator theory for congruence modular varieties. Cambridge University Press, 1987.

Hobby-McKenzie: The structure of finite algebras. AMS Contemporary Math. 76, 1996

A kérelem indoklása	3
Masters program in mathematics:. English supplement	4
1. List of courses	5
2. Examples	10
3. Personal conditions	12
4. Personal data	23
5. Language proficiency	150
6. Course descriptions	160
7. Course list: English–Hungarian	277
8. Course list: Hungarian–English	284

	MSc in Mathematics: Course list English–Hungarian
	English	Hungarian
1.	Algebraic and differential topology	Algebrai és differenciáltopológia
2.	Algebraic Topology	Algebrai topológia
3.	Algorithms I	Algoritmuselmélet I
4.	Analysis IV	Analízis IV.
5.	Analysis of time series	Idősorok elemzése I.
6.	Applicatons of operations research	Az operációkutatás alkalmazásai
7.	Applied discrete mathematics seminar	Alkalmazott diszkrét matematika szeminárium
8.	Approximation algorithms	Approximációs algoritmusok
9.	Basic algebra	Az algebra alapjai
10.	Basic geometry	Geometriai alapozás
11.	Business economics	Vállalatgazdaságtan
12.	Chapters of complex function theory	Fejezetek a komplex függvénytanból
13.	Codes and symmetric structures	Kódok és szimmetrikus struktúrák
14.	Combinatorial algorithms I	Kombinatorikus algoritmusok I.
15.	Combinatorial algorithms II	Kombinatorikus algoritmusok II.
16.	Combinatorial geometry	Kombinatorikus geometria
17.	Combinatorial number theory	Kombinatorikus számelmélet
18.	Combinatorial structures and algorithms	Kombinatorikus struktúrák és algoritmusok feladatmegoldó szeminárium
19.	Commutative algebra	Kommutatív algebra
20.	Complex functions	Komplex függvénytan
21.	Complex manifolds	Komplex sokaságok
22.	Complexity theory	Bonyolultságelmélet
23.	Complexity theory seminar	Bonyolultságelmélet szeminárium
24.	Computational methods in operations research	Operációkutatás számítógépes módszerei
25.	Continuous optimization	Folytonos optimalizálás
26.	Convex geometry	Konvex geometria
27.	Cryptography	Kriptográfia
28.	Current topics in algebra	Az algebra aktuális fejezetei
29.	Data mining	Adatbányászat
30.	Descriptive set theory	Leíró halmazelmélet
31.	Design, analysis and implementation of algorithms and data structures I	Algoritmusok és adatstruktúrák tervezése, elemzése és implementálása I.
32.	Design, analysis and implementation of algorithms and data structures II	Algoritmusok és adatstruktúrák tervezése, elemzése és implementálása II.
33.	Differential geometry I	Differenciálgeometria
34.	Differential geometry II	Differenciálgeometria II
35.	Differential Topology	Differenciáltopológia
36.	Differential Topology Problem solving	Differenciáltopológia gyakorlat
37.	Discrete dynamical systems	Diszkrét Dinamikus Rendszerek
38.	Discrete geometry	Diszkrét geometria
39.	Discrete mathematics	Diszkrét matematika
40.	Discrete mathematics II	Diszkrét matematika II
41.	Discrete optimization	Diszkrét optimalizálás
42.	Discrete parameter martingales	Diszkrét paraméterű martingálok
43.	Dynamical systems	Dinamikus rendszerek
44.	Dynamical systems and differential equations	Dinamikai rendszerek és differenciálegyenletek
45.	Dynamics in one complex variable	Komplex dinamika
46.	Ergodic theory	Ergodelmélet
47.	Exponential sums in number theory	Exponenciális összegek a számelméletben
48.	Finite geometries	Véges geometria
49.	Fourier integral	Fourier integrál
50.	Function series	Függvénysorok
51.	Functional analysis II	Funkcionálanalízis II
52.	Game theory	Játékelmélet
53.	Geometric algorithms	Geometriai algoritmusok
54.	Geometric foundations of 3D graphics	A 3D grafika geometriai alapjai
55.	Geometric measure theory	Geometriai mértékelmélet
56.	Geometric modelling	Geometriai modellezés
57.	Geometry III	Geometria III
58.	Graph theory	Gráfelmélet
59.	Graph theory seminar	Gráfelmélet szeminárium
60.	Graph theory tutorial	Gráfelmélet gyakorlat
61.	Groups and representations	Csoportok és reprezentációik
62.	Integer programming I	Egészértékű Programozás I.
63.	Integer programming II	Egészértékű Programozás II.
64.	Introduction to information theory	Bevezetés az információelméletbe
65.	Introduction to Topology	Bevezetés a topológiába
66.	Inventory management	Készletgazdálkodás
67.	Investments analysis	Befektetések elemzése
68.	LEMON library: solving optimization problems in C++	LEMON library: Optimalizációs feladatok megoldása C++-ban
69.	Lie groups and symmetric spaces	Lie-csoportok és szimmetrikus terek
70.	Linear optimization	Lineáris optimalizálás
71.	Macroeconomics and the theory of economic equilibrium	Makrogazdaságtan
72.	Market analysis	Piacok elemzése
73.	Markov chains in discrete and continuous time	Diszkrét és folytonos paraméterű Markov-láncok
74.	Mathematical logic	Matematikai logika
75.	Mathematics of networks and the WWW	WWW és hálózatok matematikája
76.	Matroid theory	Matroidelmélet
77.	Microeconomy	Mikrogazdaságtan
78.	Multiple objective optimization	Többcélfüggvényű optimalizálás
79.	Multiplicative number theory	Multiplikatív számelmélet
80.	Multivariate statistical methods	Többdimenziós statisztikai eljárások
81.	Nonlinear functional analysis and its applications	Nemlineáris funkcionálanalízis és alkalmazásai
82.	Nonlinear optimization	Nemlineáris optimalizálás
83.	Number theory 2.	Számelmélet 2.
84.	Operations research project	Operációkutatási projekt
85.	Operator semigroups	Operátorfélcsoportok
86.	Partial differential equations	Parciális differenciálegyenletek
87.	Polyhedral combinatorics	Poliéderes kombinatorika
88.	Probability and statistics	Valószínűségszámítás és statisztika
89.	Manufacturing process management	Termelésirányítás
90.	Reading course in Analysis	Analízis olvasókurzus matematikusoknak
91.	Representations of Banach-*-algebras and abstract haronic analysis	Banach*-algebrák ábrázolásai és absztrakt harmonikus analízis
92.	Rieamnn surfaces	Riemann felületek
93.	Riemannian geometry	Riemann-geometria
94.	Rings and algebras	Gyűrűk és algebrák
95.	Scheduling theory	Ütemezéselmélet
96.	Selected topics in graph theory	Válogatott fejezetek a gráfelméletből
97.	Seminar in complex analysis	Komplex függvénytani szeminárium
98.	Set theory (introductory)	Halmazelmélet
99.	Set theory I	Halmazelmélet I.
100.	Set theory II	Halmazelmélet II
101.	Special functions	Speciális függvények
102.	Statistical computing 1	Statisztikai programcsomagok 1.
103.	Statistical computing 2	Statisztikai programcsomagok 2
104.	Statistical hypothesis testing	Statisztikai hipotézisvizsgálat
105.	Stochastic optimization	Sztochasztikus optimalizálás
106.	Stochastic optimization practice	Sztochasztikus optimalizálás gyakorlat
107.	Stochastic processes with independent increments, limit theorems	Független növekményű folyamatok, határeloszlás-tételek
108.	Structures in combinatorial optimization	Kombinatorikus optimalizálási struktúrák
109.	Supplementary chapters of topology I. – Topology of singularities.	Kiegészítő fejezetek a topológiából I. – Szingularitások topológiája
110.	Supplementary Chapters of Topology II Low dimensional manifolds	Kiegészítő fejezetek a topológiából II. – Alacsony dimenziós sokaságok
111.	Topics in analysis	Fejezetek az analízisből
112.	Topics in differential geometry	Fejezetek a differenciálgeometriából
113.	Topics in group theory	Fejezetek a csoportelméletből
114.	Topics in ring theory	Fejezetek a gyűrűelméletből
115.	Topological vector spaces and Banach algebras	Topologikus vektorterek és Banach-algebrák
116.	Unbounded operators of Hilbert spaces	Nemkorlátos operátorok Hilbert téren
117.	Universal algebra and lattice theory	Univerzális algebra és hálóelmélet
	MSc in Mathematics: Course list Hungarian–English
	Hungarian	English
1.	A 3D grafika geometriai alapjai	Geometric foundations of 3D graphics
2.	Adatbányászat	Data mining
3.	Algebrai és differenciáltopológia	Algebraic and differential topology
4.	Algebrai topológia	Algebraic Topology
5.	Algoritmuselmélet I	Algorithms I
6.	Algoritmusok és adatstruktúrák tervezése, elemzése és implementálása I.	Design, analysis and implementation of algorithms and data structures I
7.	Algoritmusok és adatstruktúrák tervezése, elemzése és implementálása II.	Design, analysis and implementation of algorithms and data structures II
8.	Alkalmazott diszkrét matematika szeminárium	Applied discrete mathematics seminar
9.	Analízis IV.	Analysis IV
10.	Analízis olvasókurzus matematikusoknak	Reading course in Analysis
11.	Approximációs algoritmusok	Approximation algorithms
12.	Az algebra aktuális fejezetei	Current topics in algebra
13.	Az algebra alapjai	Basic algebra
14.	Az operációkutatás alkalmazásai	Applicatons of operations research
15.	Banach*-algebrák ábrázolásai és absztrakt harmonikus analízis	Representations of Banach-*-algebras and abstract haronic analysis
16.	Befektetések elemzése	Investments analysis
17.	Bevezetés a topológiába	Introduction to Topology
18.	Bevezetés az információelméletbe	Introduction to information theory
19.	Bonyolultságelmélet	Complexity theory
20.	Bonyolultságelmélet szeminárium	Complexity theory seminar
21.	Csoportok és reprezentációik	Groups and representations
22.	Differenciálgeometria	Differential geometry I
23.	Differenciálgeometria II	Differential geometry II
24.	Differenciáltopológia	Differential Topology
25.	Differenciáltopológia gyakorlat	Differential Topology Problem solving
26.	Dinamikai rendszerek és differenciálegyenletek	Dynamical systems and differential equations
27.	Dinamikus rendszerek	Dynamical systems
28.	Diszkrét Dinamikus Rendszerek	Discrete dynamical systems
29.	Diszkrét és folytonos paraméterű Markov-láncok	Markov chains in discrete and continuous time
30.	Diszkrét geometria	Discrete geometry
31.	Diszkrét matematika	Discrete mathematics
32.	Diszkrét matematika II	Discrete mathematics II
33.	Diszkrét optimalizálás	Discrete optimization
34.	Diszkrét paraméterű martingálok	Discrete parameter martingales
35.	Egészértékű Programozás I.	Integer programming I
36.	Egészértékű Programozás II.	Integer programming II
37.	Ergodelmélet	Ergodic theory
38.	Exponenciális összegek a számelméletben	Exponential sums in number theory
39.	Fejezetek a csoportelméletből	Topics in group theory
40.	Fejezetek a differenciálgeometriából	Topics in differential geometry
41.	Fejezetek a gyűrűelméletből	Topics in ring theory
42.	Fejezetek a komplex függvénytanból	Chapters of complex function theory
43.	Fejezetek az analízisből	Topics in analysis
44.	Folytonos optimalizálás	Continuous optimization
45.	Fourier integrál	Fourier integral
46.	Funkcionálanalízis II	Functional analysis II
47.	Független növekményű folyamatok, határeloszlás-tételek	Stochastic processes with independent increments, limit theorems
48.	Függvénysorok	Function series
49.	Geometria III	Geometry III
50.	Geometriai alapozás	Basic geometry
51.	Geometriai algoritmusok	Geometric algorithms
52.	Geometriai mértékelmélet	Geometric measure theory
53.	Geometriai modellezés	Geometric modelling
54.	Gráfelmélet	Graph theory
55.	Gráfelmélet gyakorlat	Graph theory tutorial
56.	Gráfelmélet szeminárium	Graph theory seminar
57.	Gyűrűk és algebrák	Rings and algebras
58.	Halmazelmélet	Set theory (introductory)
59.	Halmazelmélet I.	Set theory I
60.	Halmazelmélet II	Set theory II
61.	Idősorok elemzése I.	Analysis of time series
62.	Játékelmélet	Game theory
63.	Készletgazdálkodás	Inventory management
64.	Kiegészítő fejezetek a topológiából I. – Szingularitások topológiája	Supplementary chapters of topology I. – Topology of singularities.
65.	Kiegészítő fejezetek a topológiából II. – Alacsony dimenziós sokaságok	Supplementary Chapters of Topology II Low dimensional manifolds
66.	Kódok és szimmetrikus struktúrák	Codes and symmetric structures
67.	Kombinatorikus algoritmusok I.	Combinatorial algorithms I
68.	Kombinatorikus algoritmusok II.	Combinatorial algorithms II
69.	Kombinatorikus geometria	Combinatorial geometry
70.	Kombinatorikus optimalizálási struktúrák	Structures in combinatorial optimization
71.	Kombinatorikus struktúrák és algoritmusok feladatmegoldó szeminárium	Combinatorial structures and algorithms
72.	Kombinatorikus számelmélet	Combinatorial number theory
73.	Kommutatív algebra	Commutative algebra
74.	Komplex dinamika	Dynamics in one complex variable
75.	Komplex függvénytan	Complex functions
76.	Komplex függvénytani szeminárium	Seminar in complex analysis
77.	Komplex sokaságok	Complex manifolds
78.	Konvex geometria	Convex geometry
79.	Kriptográfia	Cryptography
80.	Leíró halmazelmélet	Descriptive set theory
81.	LEMON library: Optimalizációs feladatok megoldása C++-ban	LEMON library: solving optimization problems in C++
82.	Lie-csoportok és szimmetrikus terek	Lie groups and symmetric spaces
83.	Lineáris optimalizálás	Linear optimization
84.	Makrogazdaságtan	Macroeconomics and the theory of economic equilibrium
85.	Matematikai logika	Mathematical logic
86.	Matroidelmélet	Matroid theory
87.	Mikrogazdaságtan	Microeconomy
88.	Multiplikatív számelmélet	Multiplicative number theory
89.	Nemkorlátos operátorok Hilbert téren	Unbounded operators of Hilbert spaces
90.	Nemlineáris funkcionálanalízis és alkalmazásai	Nonlinear functional analysis and its applications
91.	Nemlineáris optimalizálás	Nonlinear optimization
92.	Operációkutatás számítógépes módszerei	Computational methods in operations research
93.	Operációkutatási projekt	Operations research project
94.	Operátorfélcsoportok	Operator semigroups
95.	Parciális differenciálegyenletek	Partial differential equations
96.	Piacok elemzése	Market analysis
97.	Poliéderes kombinatorika	Polyhedral combinatorics
98.	Riemann felületek	Rieamnn surfaces
99.	Riemann-geometria	Riemannian geometry
100.	Speciális függvények	Special functions
101.	Statisztikai hipotézisvizsgálat	Statistical hypothesis testing
102.	Statisztikai programcsomagok 1.	Statistical computing 1
103.	Statisztikai programcsomagok 2	Statistical computing 2
104.	Számelmélet 2.	Number theory 2.
105.	Sztochasztikus optimalizálás	Stochastic optimization
106.	Sztochasztikus optimalizálás gyakorlat	Stochastic optimization practice
107.	Termelésirányítás	Manufacturing process management
108.	Topologikus vektorterek és Banach-algebrák	Topological vector spaces and Banach algebras
109.	Többcélfüggvényű optimalizálás	Multiple objective optimization
110.	Többdimenziós statisztikai eljárások	Multivariate statistical methods
111.	Univerzális algebra és hálóelmélet	Universal algebra and lattice theory
112.	Ütemezéselmélet	Scheduling theory
113.	Vállalatgazdaságtan	Business economics
114.	Válogatott fejezetek a gráfelméletből	Selected topics in graph theory
115.	Valószínűségszámítás és statisztika	Probability and statistics
116.	Véges geometria	Finite geometries
117.	WWW és hálózatok matematikája	Mathematics of networks and the WWW