Research

Broadly, my research interest lies in the areas of Commutative Algebra and Algebraic Geometry. 

I enjoy thinking about problems pertaining to singularities in characteristic p>0. In particular, I work on problems related to Hilbert-Kunz multiplicity, Hilbert-Kunz density function,  Density functions for the second coefficient of the Hilbert-Kunz function, asymptotic growth of the Hilbert-Kunz multiplicity relative to the Hilbert Samuel multiplicity, etc. 

I work on properties of invariant ring for action of a finite group. I started working on the invariant ring of a finite p-group in characteristic p.  In particular, I studied representation with a polynomial invariant ring, ramification locus for the inclusion of the invariant ring in the polynomial ring, etc. Recently I have studied invariant ring of finite groups in characteristic 0, using characteristic p methods.

I am also interested in varieties with rich combinatorial structures (e.g. toric varieties). I like to associate the algebraic properties of the coordinate ring with the combinatorial/topological structure that is associated to the variety.