The goal of a typical combinatorial optimization problem is to efficiently find an optimal solution of a problem defined on a discrete structure (graph, directed graph, set system, poset, etc), for example a minimum cost substructure that satisfies some given properties. My research work focuses on the development of  polynomial time algorithms for graph and matroid optimization problems. 

My graph theoretic research work focuses on connectivity properties of graphs. In particular, edge splitting and detachment problems, optimal augmentation of the connectivity of graphs, orientations, extremal questions, and the corresponding algorithms. 

A matroid is a combinatorial structure that generalizes the linear independence of vectors. The theory of matroids and its algorithmic aspects are very useful is combinatorial optimization an in several branches of discrete geometry.

The theory of rigid and globally rigid graphs is an active research area with several modern applications. My research work focuses on problems in which the combinatorial properties of the given geometric objects play a central role.