Broadly speaking, I am interested in most areas of theoretical computer science. My recent focus has been on understanding computational complexity of combinatorial problems such as Clustering, Set Packing, Diversification problems and Graph problems.
Generalized Clustering problems. Since almost all of the fundamental clustering problems are hard to approximate, my focus is to understand the parameterized approximability of the general clustering problems. One concrete problem that generalizes most of the known clustering problems is Norm Clustering, where the clustering objective is any monotone norm.
Another generalization of the fundamental clustering problems is when we have additional constraints. For example, how does the complexity of these problems change under fairness, diversity and robustness constraints?
Unconditional lower bounds. I enjoy studying computational complexity of graph problems under restricted models of computation. For example, how good or bad are the standard strengthenings (Sherali-Adams, Sum-of-Squares) of the natural convex programs for these problems?
Others. I am also interested in showing conditional lower bounds such as hardness of (parameterized) approximations, etc. I have also spent some time solving problems in learning theory, space bounded derandomization, and foundations of cryptography.