Next lecture – Tuesday, September 22, 2020
In the first 10 lectures, we managed to define and construct elliptic stable envelopes
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, .
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
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)
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.
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)
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