MIT Infinite Dimensional Algebra Seminar (Spring 2022)

Meeting Time: Fridays, 3:00 PM - 5:00 PM | Location: Virtual on Zoom or on campus in Room 2-135; please contact Andrei Negut to be placed on the mailing list and to receive Zoom link and password.

Contact: Pavel Etingof, Victor Kac, and Andrei Negut

Schedule of Talks

Date and Time Speaker
February 4, 3:00 PM - 5:00 PM

(Virtual Seminar)

Catharina Stroppel
(Mathematical Institute of the University of Bonn)

Motivic Springer theory

Many interesting algebras in (geometric) representation theory arise as convolution algebras. Based on these examples we develop a general framework using Chow rings and Chow motives. Chow motives are objects in a weights structure of the triangulated derived category of motives. I will explain weight structure and weight complex functors and try to explain why it might be interesting for representation theorists.  We finally indicate formality results using motives instead of perverse sheaves.

February 11, 3:00 PM - 5:00 PM

(Virtual Seminar)

Jethro van Ekeren
(IMPA)

Chiral homology, the Zhu algebra and identities of Rogers-Ramanujan type

The notion of chiral homology of a chiral algebra was introduced by Beilinson and Drinfeld, generalising conformal blocks. The construction of a chiral algebra from a conformal vertex algebra and a smooth complex curve provides a large supply of interesting examples, but in general the chiral homology of these examples seems not to be well understood. Motivated by questions in the representation theory of vertex algebras, we study the behaviour of the chiral homology of families of elliptic curves degenerating to a nodal curve. After introducing chiral homology in general, I will explain how to develop explicit complexes to compute it in the case of interest, relate it to the Hochschild homology of the corresponding Zhu algebra, and establish links with identities of Rogers-Ramanujan type and their generalisations. (Joint work with R. Heluani)

February 18, 3:00 PM - 5:00 PM

(Virtual Seminar)

Andrei Negut
(MIT Mathematics)

Generators and relations for quantum loop groups

I will describe a program that uses shuffle algebras to yield generators-and-relations presentations for quantum loop groups. The main idea is that the necessary relations are dual to the so-called wheel conditions that describe the shuffle algebras in question, and we will use this to get a complete presentation of two interesting algebras that arise in geometric representation theory: K-theoretic Hall algebras of quivers, and Hall algebras of coherent sheaves on curves over finite fields (the latter project joint work with Francesco Sala and Olivier Schiffmann).

February 25, 3:00 PM - 5:00 PM

March 4, 9:00 AM - 11:00 AM

(Virtual Seminar Special Time)

Sylvain Carpentier
(Columbia University)

Quantization of integrable differential difference equations

We present a new approach to the problem of quantising integrable systems of differential-difference equations. The main idea is to lift these systems to systems defined on free associative algebras and look for the ideals there that are stabilized by the new dynamics. In a reasonable class of candidate ideals, there are typically very few that are invariant for the first equation in the hierarchy. Once these ideals are picked the challenge is to prove that the whole hierarchy of equations stabilizes them. We will discuss these ideas using as a key example the hierarchy of the Bogoyavlensky equation.
This is a joint work with A. Mikhailov (Leeds) and J. P. Wang (U. of Kent). To be published soon.

March 11, 3:00 PM - 5:00 PM

March 18, 3:00 PM - 5:00 PM

March 25, 3:00 PM - 5:00 PM

April 1, 3:00 PM - 5:00 PM

April 8, 3:00 PM - 5:00 PM

April 15, 3:00 PM - 5:00 PM

April 22, 3:00 PM - 5:00 PM

April 29, 3:00 PM - 5:00 PM

May 6, 3:00 PM - 5:00 PM

May 13, 3:00 PM - 5:00 PM

May 20, 3:00 PM - 5:00 PM

May 27, 3:00 PM - 5:00 PM

June 3, 3:00 PM - 5:00 PM

June 10, 3:00 PM - 5:00 PM

Archived Seminar Webpages

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