I'm a reclusive toad living in the swamp of algebraic geometry.  Occasionally when it rains, I take a stroll on the lane to combinatorics, and get lost in the symmetrical highland of representation theory.  I also hold on to my umbrella and drift to where the wind blows us  -- the eroded cliff of category theory, or the drifting dunes of topology. My favorite season is the spring.

I have been working with the Hilbert scheme of points on non-reduced plane curves. For example, take the x-axis with multiplicity 3, y^3=0, and consider the Hilbert scheme of n points on it, Hilb^n({y^3=0}).  This is defined to be the moduli space of ideals of C[x,y]/(y^3) that have colength n.  The Hilbert schemes of points on the singular plane curves have interesting geometry, and their cohomologies are conjected to be related to the Khovanov-Rozansky homology. Currently I'm interested in studying the homologies of the Hilbert schemes of points on non-reduced curves and their relation with the Nakajima operators. 

My advisor is professor Eugene Gorsky. 

I'm in my 4th year of graduate school at the math department of UC Davis. I will be on the job market this Fall 2024. Click to see my CV.

I tried and failed to take a photo with the physics department cat for this website. I'll keep trying before I graduate.