okuon_lect20

Professor Andrei Okounkov (Skoltech, Columbia Univ.)
will deliver a series of lectures titled

“Enumerative geometry and geometric representation theory”

Next lecture – Tuesday, September 22, 2020


The link to access the Coursehttps://zoom.us/j/92596832934
Course whiteboardOneNote
Course announcementsTelegram Messenger

Schedule:

  •   1st lecture / May 13 / video / whiteboard_pdf (3.6 MB)
  •   2nd lecture / May 20 / video / whiteboard_pdf (3.6 MB)
  •   3rd lecture / May 27 / video / whiteboard_pdf (3.6 MB)
  •   4th lecture / June 3 / video / whiteboard_pdf (3.6 MB)
  •   5th lecture / June 17 / video / whiteboard_pdf (4.3 MB)
  •   6th lecture / June 24 / video / whiteboard_pdf (3.2 MB)
  •   7th lecture / July 1 / video / whiteboard_pdf (5.3 MB)
  •   8th lecture / July 8 / video / whiteboard_pdf (3.3 MB)
  •   9th lecture / July 15 / video / whiteboard_pdf (3.4 MB)
  • 10th lecture / July 22 / video / whiteboard_pdf (4.2 MB)
  • In the first 10 lectures, we managed to define and construct elliptic stable envelopes

  • 11th lecture / July 29 / video / whiteboard_pdf (4.6 MB)
  • Plan for Jul 29:
    1. Examples of stable envelopes: projective spaces, hypertoric varieties, Grassmannians,…
    2. Basic properties of stable envelopes: triangle lemma, Yang-Baxter equation, duality, .

  • 12th lecture / August 5 / video / whiteboard_pdf (3.4 MB)
  • 13th lecture / August 12 / video / whiteboard_pdf (3.2 MB)
  • 14th lecture / August 19 / video / whiteboard_pdf (4.5 MB)
  • 15th lecture / August 26 / video / whiteboard_pdf (3.8 MB)
  • The plan is to discuss quantum groups associated to the quiver with one vertex and one loops, that is, to double loops in gl(1). I will assume some basic familiarity with Nakajima quiver varieties. If you need an elementary introduction to those, one possible source is , among many others

  • 16th lecture / September 2 / video / whiteboard_pdf (4.2 MB)
  • The plan for Sep 2: (1) Lagrangian Steinberg correspondences commute with R-matrices in cohomology, (2) classical R-matrix for \hat \hat gl(1), (3) Virasoro algebra and full R-matrix for \hat \hat gl(1)

  • 17th lecture / September 8 / video / whiteboard_pdf (4.2 MB)
  • 18th lecture / September 16 / video / whiteboard_pdf (3.2 MB)
  • Regarding the discussion at the very end of the lecture, it may be instructive to watch the old video . We won’t be pursuing the connections with ILW and other objects discussed in that video in this series of lectures.

  • 19th lecture / Tuesday, September 22 / 17:30 – 19:00 (Moscow time)
  • Due to conflict with other elements of the Fall semester schedule, the lectures will be on Tuesdays same time starting next week, that is, starting Tuesday September 22.
    September 22, there will be a general and introductory discussion of what is enumerative geometry and how it interacts with integrable systems (as seen from my personal point of view, no general overview attempted)

  • 20th lecture / Tuesday, September 29 / 17:30 – 19:00 (Moscow time)
  • Tuesday September 29 we will have a guest lecture about virtual classes by Prof. Melissa Liu. Same time, that is, 17:30 Moscow time, 10:30 New York City time

Abstract:

  • The goal of this course it to explain how a broad class of enumerative problems (of origin in modern mathematical physics) may be solved in the language of geometric representation theory. We will start from the basics, including equivariant K-theory and equivariant elliptic cohomology, then set up the quantum groups, and then proceed with the enumerative applications

Language:

  • English

Note:

  • This series of lectures will be video-recorded and made available online