Representations of p-adic groups and applications

Jessica Fintzen (Cambridge/Duke/IAS)

08-Sep-2020, 14:30-15:30 (4 years ago)

Abstract: The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the construction of all (irreducible, smooth, complex) representations of p-adic groups.

I will provide an overview of our understanding of the representations of p-adic groups, with an emphasis on recent progress.

I will also outline how new results about the representation theory of p-adic groups can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p, which is joint work with Sug Woo Shin. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.

algebraic geometrynumber theory

Audience: researchers in the topic

( slides )

Comments: Note the this talk will take place at 10:30 rather than 16:30 (Eastern time).


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Organizers: Edgar Costa*, Siyan Daniel Li-Huerta*, Bjorn Poonen*, David Roe*, Andrew Sutherland*, Robin Zhang*, Wei Zhang*, Shiva Chidambaram*
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