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.

I am also working on a project joint with Benjamin Gammage, Justin Hilburn and others on elliptic analogues of Coulomb branches for 5D SUSY gauge theories.

Other interests include: The classical and quantum double-elliptic integrable system, Calogero-Moser particles on orbifolds, Schur-Weyl duality for Cherednik algebras, …

Publications

Joint with Martin Luu: Langlands Parameters of Quivers in the Sato Grassmannian. Published in Communications in Mathematical Physics. arXiv preprint.

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.

Presentations

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.