MIT Infinite Dimensional Algebra Seminar (Fall 2022)

Meeting Time: Fridays, 3:00 PM - 5:00 PM | Location: Room 2-135, unless otherwise specified; 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
September 9, 3:00 PM - 5:00 PM

(Room 2-135)

Victor Kac
(MIT)

Unitary representations of vertex algebras

I will explain the definition of unitarity of a representation of a conformal vertex algebra and describe the classification of unitary representations of minimal quantum affine W-algebras. I will also explain how to compute the characters of these representations.

September 16, 3:00 PM - 5:00 PM

(Room 2-135)

Leonid Rybnikov
(Harvard University)

sl_2-opers and arc diagrams

We define a natural, purely geometrical bijection between the set of monodromy-free sl_2-opers (aka projective structures) on the projective line with the prescribed type of regular singularities at prescribed real marked points and the set of arc diagrams of Frenkel-Kirillov-Varchenko. The former set indexes the solutions of Bethe ansatz equations for the Gaudin model (according to Feigin and Frenkel), while the latter one indexes the canonical base in a tensor product of U_q(sl_2)-modules (via the Schechtman-Varchenko isomorphism). Both sets carry a natural action of the cactus group, i.e., the fundamental group of the real Deligne-Mumford space of stable rational curves with marked points. We prove that our bijection is compatible with this cactus group action. Moreover, this cactus group action coincides with that on an appropriate tensor product of sl_2-crystals coming from the coboundary category formalism (joint work with Nikita Markarian).

September 23, 3:00 PM - 5:00 PM

(Room 2-135)

no seminar (Vogan conference)

September 30, 3:00 PM - 5:00 PM

(Room 2-135)

no seminar (retreat weekend)

October 7, 3:00 PM - 5:00 PM

(Room 2-135)

/td>
Vasily Krylov
(MIT Mathematics)

October 14, 3:00 PM - 5:00 PM

(Room 2-135)

Maria Gorelik
(UC Berkeley)

October 21, 3:00 PM - 5:00 PM

(Room 2-135)

Ben Davison
(University of Edinburgh)

October 28, 3:00 PM - 5:00 PM

(Room 2-135)

Arun Kanaan
(MIT Mathematics)

November 4, 3:00 PM - 5:00 PM

(Room 2-135)

Brian Williams
(Northeastern University)

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

(Room 2-135)

no seminar (holiday)

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

(Room 2-135)

Iva Halacheva
(The University of Melbourne)

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

(Room 2-135)

no seminar (holiday)

December 2, 3:00 PM - 5:00 PM

(Room 2-135)

/td>
Ilya Dumansky
(MIT Mathematics)

December 9, 3:00 PM - 5:00 PM

(Room 2-135)

Alexey Borodin
(MIT Mathematics)

Archived Seminar Webpages

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