MIT Infinite Dimensional Algebra Seminar

MIT Infinite Dimensional Algebra Seminar (Fall 2026)

Meeting Time: Friday, 3:00-5:00 p.m. | Location: 2-135

Meeting ID
918 0043 8944

For the Passcode, please contact Pavel Etingof at etingof@math.mit.edu.

Please note that the seminar will run on occasion throughout this Fall semester.

Date

Speaker

Title & Abstract

September 18

Ilya Dumanski
(SLMath)

Chiralization of integrable systems

Given a symplectic variety X, one can define its chiral quantization — a sheaf of vertex algebras, which deforms the jet bundle of X. The study of such structures is motivated by mathematical physics. Classification, or even construction, of chiral quantizations is a hard problem, with a lot of recent progress. In this talk, we address this problem in the case when X is a smooth completely integrable system. We use the method of formal geometry (as applied by Fedosov and Bezrukavnikov—Kaledin in the study of ordinary quantizations) to construct chiral quantizations in this case. Then we discuss the possibility of chiralizing the BFN Coulomb branches using this technique

Video (Requires MIT Login)

November 13

Tudor Pădurariu
(University of Bonn)

Abelian quasi-BPS categories

I will report on joint work in progress with Sabin Cautis and Yukinobu Toda. The Grothendieck group of the Hall category of a quiver is isomorphic to a positive half of the quantum affine algebra corresponding to the quiver. We show that two structures on the Hall category are compatible: a perverse coherent t-structure and a filtration by window categories.

In particular, we construct t-structures on the so-called quasi-BPS categories, which generate Hall categories. We thus obtain a refinement of the total BPS cohomology of the quiver, whose dimension is the value at one of the Kac polynomial of the quiver, in terms of nilpotent orbits.

I will discuss examples of quasi-BPS categories for finite-type quivers, where they may be compared with categories of representations of KLR algebras, and for the Jordan quiver. As a corollary, we prove a conjecture of Gorsky–Negut about generators of the category of coherent sheaves on the commuting stack.

Archived Seminar Webpages

Date	Speaker	Title & Abstract
September 18	Ilya Dumanski (SLMath)	Chiralization of integrable systems Given a symplectic variety X, one can define its chiral quantization — a sheaf of vertex algebras, which deforms the jet bundle of X. The study of such structures is motivated by mathematical physics. Classification, or even construction, of chiral quantizations is a hard problem, with a lot of recent progress. In this talk, we address this problem in the case when X is a smooth completely integrable system. We use the method of formal geometry (as applied by Fedosov and Bezrukavnikov—Kaledin in the study of ordinary quantizations) to construct chiral quantizations in this case. Then we discuss the possibility of chiralizing the BFN Coulomb branches using this technique Video (Requires MIT Login)
November 13	Tudor Pădurariu (University of Bonn)	Abelian quasi-BPS categories I will report on joint work in progress with Sabin Cautis and Yukinobu Toda. The Grothendieck group of the Hall category of a quiver is isomorphic to a positive half of the quantum affine algebra corresponding to the quiver. We show that two structures on the Hall category are compatible: a perverse coherent t-structure and a filtration by window categories. In particular, we construct t-structures on the so-called quasi-BPS categories, which generate Hall categories. We thus obtain a refinement of the total BPS cohomology of the quiver, whose dimension is the value at one of the Kac polynomial of the quiver, in terms of nilpotent orbits. I will discuss examples of quasi-BPS categories for finite-type quivers, where they may be compared with categories of representations of KLR algebras, and for the Jordan quiver. As a corollary, we prove a conjecture of Gorsky–Negut about generators of the category of coherent sheaves on the commuting stack.