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Soergel bimodules, matrix factorizations and Hilbert schemes

Event Category:
Representation Theory
Alexei Oblomkov

My talk is based on joint work with L. Rozansky. In our work we study a category MFn of matrix factorizations that categorifies the finite Hecke algebra. I will explain a construction of a fully faithful functor from
SBimn to MFn. We compose this functor with the Chern functor CH: MFn → Cohper(Hilbn(C2)) to obtain a two-periodic complex of sheaves Sb for a braid b ∈ Brn such that H*(Sb) is equal to the triply graded homology of b. Some explicit examples of Sb will be shown.

Monday, February 12, 2024 - 2:30pm
LGRT 1621