I am an algebraic geometer with broader interests in algebra, representation theory, and number theory. Being an algebraic geometer means that I study algebraic varieties—spaces of solutions of algebraic equations. I am interested in classical algebraic geometry, enumerative geometry, deformation theory, algebraic stacks, derived categories, among other things.
A common theme in much of my work is to understand varieties by studying the collection of all related varieties at once, using the remarkable feature that such a collection itself forms an algebraic variety (or something close to it), called a “moduli space”. I have worked on moduli spaces of algebraic curves, surfaces, maps, vector bundles, and stability conditions.
With Asilata Bapat and Tony Licata, I am thinking about various aspects of stability conditions on some triangulated categories. We finished a draft of a proposed construction of a compactification of this space with full details for the A2 and A1-hat cases. The Farey sequence makes an appearance!
Anand Patel, Eduard Duryev, and I finished a paper about some fascinating variational and enumerative questions arising from a simple construction related to linear projections. Answers to some of these enumerative questions fit the sequence A001181 on OEIS, but we are stumped as to why!
In Semester 2 of 2020, I am running a special topics course Foundations of algebraic geometry.
Want to see the courses at the maths department and their prerequisites? Look at this graph!