Research Interests

Broadly speaking, my research interests are in geometric representation theory. In my current research, I am investigating how MV polytopes and similar constructions unify various geometric/algebraic/combinatorial constructions related to affine Kac-Moody groups.

I am also interested in automorphic forms, especially automorphic forms on Kac-Moody groups. In particular, I am interested in studying how the geometric/combinatorial constructions in representation theory can give rise to number theoretic formulas.

Here are a few keywords that make me perk up: affine Kac-Moody groups (a.k.a loop groups), Mirkovi\'c Vilonen (MV) polytopes, MV cycles, affine Grassmannians, geometric Satake equivalence, quantum affine algebras, crystals, canonical/global basis, PBW basis, MV basis, quasimaps, semiinfinite flag variety, preprojective algebras, Satake isomorphism, Casselman-Shalika formula.

Papers

• Double MV Cycles and the Naito-Sagaki-Saito Crystal - submitted [arxiv link].
• Affine PBW Bases and MV Polytopes in Rank 2 - joint with Peter Tingley - to appear in Selecta Mathematica, N.S. [arxiv link].