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Presented By: RTG Seminar on Number Theory - Department of Mathematics

RTG NT: Affine Soergel bimodules and flattening

Calvin Yost-Wolff

Abstract: Soergel bimodules categorify the Hecke algebra of a Coxeter group and have been useful in studying Kazhdan-Lusztig polynomials. Khovanov used Soergel bimodules for the symmetric group to construct a triply graded link invariant which is notoriously difficult to compute. Recently, Mellit and Hogancamp computed this invariant for torus links. Affine Soergel bimodules are an analogous categorification of affine Hecke algebras. Categorifying the flattening homomorphism from the affine Hecke algebra to the finite Hecke algebra could shed light on this computation of Mellit and Hogancamp. I will explain approaches to defining this functor and conjectures involving this functor and the categorical center of affine Soergel bimodules.

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