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Caltech

Postdoctoral Math Seminar

Tuesday, November 27, 2018
6:00pm to 7:00pm
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Linde Hall 387
The factorizable derived geometric Satake equivalence
Justin Campbell, Department of Mathematics, Caltech,
The geometric Satake equivalence, due to Ginzburg and Mirkovic-Vilonen, identifies spherical perverse sheaves on the affine Grassmannian with representations of the Langlands dual group. It is an equivalence of symmetric monoidal abelian categories, which is compatible in some sense with the factorization structure of the affine Grassmannian. The equivalence does not hold at the level of derived categories, and Bezrukavnikov-Finkelberg showed how to enhance the spectral side to obtain a derived geometric Satake equivalence, although their methods are not compatible with factorization. I will explain how to make sense of the spectral Hecke category factorizably, which allows us to reprove the derived geometric Satake equivalence independently of Bezrukavnikov-Finkelberg's work, and to formulate an enhanced Hecke compatibility for the global geometric Langlands equivalence.
For more information, please phone 626-395-4335 or email [email protected].