"Gaitsgory gives an informal introduction to the geometric Langlands program. This is a new and very active area of research which grew out of the theory of automorphic forms and is closely related to it. Roughly speaking, in this theory we everywhere replace functionsālike automorphic formsāby sheaves on algebraic varieties; this allows us to use powerful methods of algebraic geometry in order to construcut "automorphic sheaves.""
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Joseph Bernstein and Stephen Gelbart:
https://en.wikiquote.org/wiki/Geometric_Langlands_correspondence
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Geometric Langlands correspondence
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