Meeting Time: Friday, 3:005:00 p.m.  Location: 2135
Contact: Pavel Etingof and Victor Kac
Zoom Link: https://mit.zoom.us/j/94469771032
Meeting ID
944 6977 1032
For the Passcode, please contact Pavel Etingof at etingof@math.mit.edu.
Date  Speaker  

February 9  Elijah Bodish (MIT) 
Spin link homology and webs in type B In their study of GL(N)GL(m) Howe duality, CautisKamnitzerMorrison observed that the GL(N) ReshetikhinTuraev link invariant can be computed in terms of quantum gl(m). This idea inspired Cautis and LaudaQueffelecRose to give a construction of GL(N) link homology in terms of KhovanovLauda's categorified quantum gl(m). There is a Spin(2n+1)Spin(m) Howe duality, and a quantum analogue which was first studied by Wenzl. In the first half of the talk I will explain how to use this duality to compute the Spin(2n+1) link polynomial, and present calculations which suggest that the Spin(2n+1) link invariant is obtained from the GL(2n) link invariant by folding. In the second part of the talk, I will introduce the parallel categorified constructions and explain how to use them to define Spin(2n+1) link homology. This is based on joint work in progress with Ben Elias and David Rose. Audio Transcript (Requires MIT Login) 
February 16  Yasuyuki Kawahigashi (University of Tokyo) 
Quantum 6jsymbols and braiding I will explain certain 4tensors appearing in studies of twodimensional topological order from a viewpoint of subfactor theory of Jones and alphainduction there, which is a tensor functor arising from a modular tensor category and a Frobenius algebra in it. They are understood with quantum 6jsymbols and braiding. Audio Transcript (Requires MIT Login) 
February 23  Kenta Suzuki (MIT) 
Affine KazhdanLusztig polynomials on the subregular cell: with an application to character formulae (joint with Vasily Krylov) I will explain the computation of special values of parabolic affine inverse KazhdanLusztig polynomials, which give explicit formulas for certain irreducible representations of affine Lie algebras that generalize Kac and Wakimoto's results. By Bezrukavnikov's equivalence, the canonical basis in the subregular part of the antispherical module can be identified with irreducible objects in the exotic tstructure on the equivariant derived category of the subregular Springer fiber. We describe the irreducible objects explicitly using an equivariant derived McKay correspondence. In doing so, we identify the module with a module Lusztig defines, which compatibly extends to the regular cell. Audio Transcript (Requires MIT Login) 
March 1  Vadim Vologodskii 

March 8  Zhiwei Yun (MIT) 

March 15  Ivan Cherednik (University of North Carolina at Chapel Hill) 
From DAHA superpolynomials for algebraic links to motivic ones The focus will be on a recent construction of the motivic superpolynomials for arbitrary singularities (multibranch and nonsquarefree). They will be introduced from scratch, which includes the definition of varieties of torsionfree sheaves of any rank over curve singularities. Our motivic superpolynomials are q,t,ageneralizations of orbital integrals associated with Affine Springer Fibers of type A in the case of the most general characteristic polynomials. I will not use the theory of ASF. The key conjecture is their coincidence with the DAHA superpolynomials of the corresponding (colored) algebraic links. The latter (due to CherednikDanilenko) will be defined. This coincidence can be seen as a highlevel Shuffle Conjecture. As an application, the DAHA vertex will be considered and its relation to the qtheory of Riemann’s zeta. Also, q,t,adeformations of the modified rhoinvariants of algebraic knots will be discussed; classically, rho is defined via the AtiyahPatodiSinger eta invariant, but I will need only some formulas in this talk. See https://arxiv.org/abs/2304.02200. 
March 22  Do Kien Hoang (Yale University) 

March 29  Spring Break 

April 5  Dan Freed 

April 12  Andrei Neguț (MIT) 

April 19  Alexandre Goncharov 

April 26  Milen Ykimov 

May 3  Roman Bezrukavnikov (MIT) 

May 10  Ivan Loseu 