March 8, p.
Ivan Loseu University of Toronto Harish-Chandra bimodules over quantized symplectic singularities We study a certain category of bimodules over a filtered algebra quantizing the algebra of functions on a conical symplectic singularity. The bimodules we care about are so called Harish-Chandra bimodules. This notion first appeared in the case of universal enveloping algebras of semisimple Lie algebras in the work of Harish-Chandra on representations of the corresponding complex Lie groups.
Since then it was generalized to filtered quantizations of algebras of functions on affine Poisson varieties. We will see that these irreducible bimodules are in one-to-one correspondence with the irreducible representations of a suitable finite group.
The talk is based on arXiv I will not assume any preliminary knowledge of conical symplectic singularities, their quantizations etc. March 15, p. I will then explain how this definition can be refined in various ways to accommodate in particular the 2-categorical extension of Etingof-Kazhdan quantisation which Andrea Appel and I recently obtained. This is joint work with Andrea Appel. March 22, p. March 29, p. Spring break April 5, p. Zhiwei Yun MIT Endoscopy for Hecke category and character sheaves Hecke categories are geometric incarnations of Hecke algebras, and they play an important role in the classification of irreducible representations of finite groups of Lie type.
We consider a version of the Hecke category for the reductive group G with prescribed monodromy under the left and right actions of the maximal torus. We show that this monoidal category can essentially be identified with the usual Hecke category with trivial torus monodromy for an endoscopic group H of G, which is a reductive group of smaller dimension sharing a maximal torus with G but is not necessarily a subgroup of G.
As a consequence, we show that character sheaves on G and on H are closely related. Joint work with G. April 12, p. Alexei Borodin MIT Stochastic vertex models The goal of the talk is to survey recently discovered and rapidly developing interplay between solvable vertex models, symmetric functions, and probability. Evidence for a highly opaque large-scale galaxy void at the end of reionization. A Quantitative Approach. Supersolid stripe crystal from finite-range interactions on a lattice. Problem Structures in the Theory and Practice of Superiorization.
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