On the Langlalands correspondence for curves over local fields

On the Langlalands correspondence for curves over local fields

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David Kazhdan, Hebrew University of Jerusalem

Zoom link:  https://princeton.zoom.us/j/99136657600

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Let F be a local field, X a smooth complete curve over F and Bun the moduli stack of principal G bundles on X. In the first part of my talk I outline a definition of the algebra T of Hecke operators T_x acting on the Hilbert space of half-forms on Bun. In the second part I restrict myself to the case when F is the field of complex numbers and describe the interplay between T and the algebra of differential operators on Bun.

My talk is on a joint work with P.Etingof and E.Frenkel.