I am usually thinking about elliptic analogues of many classically defined integrable systems and constructions in algebraic geometry.
Currently I am working on a project joint with David Ben-Zvi and Tom Nevins on proving the RS-2D Toda correspondence via a non-commutative Fourier-Mukai transform on difference modules akin to the proof of the KP-CM correspondence from the first two authors.
Other projects that are in the works:
Finding a difference-reflection module construction of the Ruijsenaars-Schneider analogous to the differential-reflection construction for the Calogero-Moser system.
Other interests include: The classical and quantum double-elliptic integrable system, Calogero-Moser particles on orbifolds, Schur-Weyl duality for Cherednik algebras, …
Spectral Description of the Spin Ruijsenaars-Schneider System. Submitted for publication. arXiv prepint.
(work in progress) Joint with Martin Luu: Some Aspects of Virasoro Constraints for Drinfeld-Sokolov Hierarchies.
Below are some slides and from recent talks. If you’ve seen a talk of mine, and would want a copy of my lecture notes feel free to email me and I can send them over!
Slides from the CMS Special session on Algebraic Geometry and Representation Theory
Packages and scripts
Below are some mathematica notebooks and python scripts I wrote to help with calculations and visualizations
A mathematica notebook for siimulations of the rational Calogero Moser system.
A mathematica notebook to do calculations for pseudo-differential operators.
(forthcoming) A python package to do calculations on Laurent series, and apply the Hukuhara-Levelt-Turrittin algorithm to irregular singular connections.