Abstract
The local Langlands conjecture seeks to parameterize irreducible representations of a p-adic reductive group in terms of Galois-theoretic data. The categorical form of the conjecture, as posed by Fargues-Scholze, upgrades local Langlands to an equivalence between categories. Besides being a marvelous demonstration of the link between arithmetic and geometry, the categorical conjecture elegantly explains many features of the set-theoretic conjecture. The goal of this seminar is to carefully explain the categorical conjecture and the latest attacks on it.
Notes
Notes from the seminar (warning, these are quite rough)
Info and Schedule
The seminar is held Fall 2026, Wednesdays 10-11:30 am in Mathematics Hall at Columbia University. It is led by Jared Weinstein.
Sep. 16: Local Class Field theory and the theorem of Harris-Taylor
Sep. 23: The (set-theoretic) local Langlands correspondence
Sep. 30: Geometric Langlands