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Tate's thesis in the de Rham setting

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Speaker: 
Samuel Raskin
Affiliation: 
University of Texas, Austin
Date: 
Mon, 2020-06-22 20:00 - 20:55

This is joint work with Justin Hilburn. We will explain a theorem showing that D-modules on the Tate vector space of Laurent series are equivalent to ind-coherent sheaves on the space of rank 1 de Rham local systems on the punctured disc equipped with a flat section. Time permitting, we will also describe an application of this result in the global setting. Our results may be understood as a geometric refinement of Tate's ideas in the setting of harmonic analysis. They also may be understood as a proof of a strong form of the 3d mirror symmetry conjectures: our results amount to an equivalence of A/B-twists of the free hypermultiplet and a U(1)-gauged hypermultiplet.

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