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On the p-adic Langlands program

Florian Herzig (U. of Toronto)

Location:  Hill 705
Date & time: Friday, 08 November 2019 at 4:00PM - 5:00PM

Abstract: The "classical" Langlands correspondence relates n-dimensional Galois representations to representations of the p-adic general linear group GL_n(Q_p), both over the field of complex numbers. The mod p (resp. p-adic) Langlands correspondence is an analogue of this correspondence over a field of characteristic p (resp. over a p-adic field). So far it has only been established in dimension n \le 2, with powerful applications to the modularity of Galois representations. In this talk I will give motivation and discuss some earlier developments as well as some recent progress for n > 2. No background in the Langlands program will be assumed.

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