Seminar: representations of affine Kac-Moody algebras at the critical level.

Time: generally 4-6.15pm, Thursdays, at MIT, room 26-168. If there's a related Math activity scheduled at MIT at 4 (such as colloquium) or elsewhere, the seminar may move to 5.45-8pm.

Organized by Roman Bezrukavnikov, Pavel Etingof, Ivan Losev, Leonid Rybnikov, David Yang, and Zhiwei Yun.

This is a graduate learning seminar, where students give lecture advised by one of the seminar organizers, most likely Prof. Losev. Please contact Prof. Losev if you'd like to give a talk.

This seminar is a successor of the series of seminars organized by some organizers in 2013-2017. In particular, these seminars played an important role in Prof. Etingof's professional growth: he progressed from this to this and finally, even to this. Unfortunately, the pause in the seminar series brought him to this state... Let's help Prof. Etingof to get back to his former shape!

This year seminar is going to concetrate on Edward Frenkel's book on the Langlands correspondence for loop groups. The preliminary plan is to go over chapters 2-8, including free field realizations, Wakimoto modules, and the center at the critical level (with more time permitting).

Prerequisites include basic knowledge of the BGG category O (Etingof's course from Fall 2023 or the first three lectures here should do) and basics on (affine) Kac-Moody algebras and their integrable representations (Chapters 1-7 and 9 from the Kac Infinite dimensional Lie algebras book should do, and so should the class taught by Rybnikov in Fall 2023).

Schedule:

  • Feb 8, 5.45-8pm: Ilya Dumanski speaks on Chapter 2. Notes.
  • Feb 15, 5.45-8pm: Ilya finishes on Chapter 2 and Hamilton Wan starts on Sections 3.1-3.3. Ilya's notes.
  • Feb 22, 5.45-8pm: Hamilton continues on Section 3.2-3.3.1.
  • In addition to pizza slices, seminar participants are welcome to enjoy Kostant slices that are going to be important for subsequent lectures. These slices can be enjoyed, for example, by reading this note.
  • Feb 29, 5.45-8pm: Hamilton finishes Section 3.3 and Vanya Karpov starts on Sections 3.4 and 3.5. Complete notes for all Hamilton's talks.
  • Mar 7, 5.45-8pm: Vanya speaks on Sec 3.5. Complete notes for Vanya's two talks.
  • Mar 14, 5.45-8pm: Ekaterina Bogdanova starts to speak on Chapter 4, notes.
  • Untimely warning: a scary monster was seen in the streets of Cambridge (observed by Daishi who escaped unharmed). The monster catches the speakers who don't do a good job preparing for their talks and devours them.
  • Mar 21, 5.45-8pm: Katya finishes and Daishi Kiyohara starts on Chapter 5. A note on the universal enveloping algebras for commutative vertex algebras to be used in Katya's talk. Notes for Katya's talk.
  • Mar 28: no meeting -- MIT's Spring break. Some music for relaxation...
  • Apr 4: 5.45-8pm: Daishi finishes. Notes for both Daishi's talks. A note on formal loops.
  • The first note on chiral differential operators.
  • Apr 11: 5.45-8pm: Zeyu Wang speaks on 6.1 and 6.2.
  • Apr 18: 5.45-8pm: Zeyu finishes, complete notes. Kenta Suzuki starts on Sec 6.3.
  • The second note on chiral differential operators.
  • Apr 25: 5.45-8pm: Kenta continues on Secs 6.3-6.4. Complete notes.
  • May 2: 5.45-8pm: Daniil Klyuev speaks on Sections 7.1 and 7.2.
  • May 6 (Monday!): 5.45-8pm in 2-449: Daniil finishes and Calder Morton-Ferguson potentially starts on Sec 7.3. Daniil's complete notes.
  • May 9: 5.45-8pm in 26-168: Calder speaks on 7.3.4 and 8.1.1-8.1.3. Complete notes.
  • May 13: 5.45-8pm in 2-449: Vasya Krylov speaks on the remainder of 8.1 and 8.2. Notes.
  • May 16: 5.45-8pm in 26-168 (a.k.a. the last!): Vasya covers 8.2.2-8.2.5. Notes.
  • THE END!