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Nilpotent Slodowy slices and W-algebras
To any vertex algebra one can attach in a canonical way a certain Poisson variety, called the associated variety. Nilpotent Slodowy slices appear as associated varieties of admissible (simple) W-algebras...
Oct 29, 2020
Borcherds algebras and 2d string theory
Borcherds Kac-Moody (BKM) algebras are a generalization of familiar Kac-Moody algebras with imaginary simple roots. On the one hand, they were invented by Borcherds in his proof of the monstrous...
Oct 29, 2020
Homological mirror symmetry for the universal centralizers
I will present recent work (to appear soon) on the homological mirror symmetry about the universal centralizers $J_G$, for any complex semisimple Lie group $G$. The A-side is a partially...
Nov 05, 2020
Equivariant Elliptic Cohomology
The subject of equivariant elliptic cohomology finds itself at the interface of topology, string theory, affine representation theory, singularity theory and integrable systems. These connections were already known to the...
Nov 19, 2020
q-Opers, QQ-Systems, and Bethe Ansatz
We introduce the notions of (G,q)-opers and Miura (G,q)-opers, where G is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a...
Dec 03, 2020
3d A-twist and analytic continuation of path integrals II
3d A-twist and analytic continuation of path integrals II
Feb 27, 2020
Coordinate Charts on Character Varieties via Non-abelianization
Classical work by Thurston in the theory of surfaces gives symplectic co-ordinate charts on Teichmüller space, associated to quadratic differentials. Motivated by wall crossing in 4d field theories Gaiotto, Moore...
Feb 27, 2020
Affine Beilinson-Bernstein at the critical level for GL_2
There has long been interest in Beilinson-Bernstein localization for the affine Grassmannian (or affine flag variety). First, Kashiwara-Tanisaki treated the so-called negative level case in the 90's. Some ten years...
Mar 05, 2020
Homology of the affine Grassmannian and quantum cohomologies
Let G be a complex reductive group, and X be any smooth projective G-variety. In this talk, we will construct an algebra homomorphism from the G-equivariant homology of the affine...
Mar 05, 2020
Holomorphic-topological twists and TFT
I'll explain the TFT perspective on holomorphic-topological twists of 3d N=4 and 4d N=2 theories, and outline some connections between the topics discussed in Justin and Davide's previous lectures, and...
Mar 12, 2020