Research

It's fine to work on any problem, so long as it generates interesting 

mathematics along the way - even if you don't solve it at the end of the day.

-Andrew Wiles      

Research Interests

I study braid varieties which are an interesting class of smooth affine algebraic varieties which include particularly well-known Lie theoretic varieties such as open Richardson and positroid varieties. I mainly focus my attention on the computation of its cohomologies using various techniques including methods from cluster algebras. These objects peaked my interest due to the connections with Khovanov-Rozansky homology (HHH).

Cluster algebras are a rather exciting commutative algebra which arise from "seeds" containing information called cluster variables and an exchange matrix (or quiver), through an iterative process called mutation one can recover the remaining cluster variables. We define the cluster algebra to be the subring generated by all the cluster variables. Moreover, these cluster variables have a rather nice combinatorial structure that is fascinating in its own right. 

I also find moduli spaces and representation theory interesting.

Papers and Preprints

(To appear in Contemporary Mathematics issue on Algebraic Structures in Knot Theory)

Presentations

Conferences Attended