Real local Langlands as geometric Langlands on the twistor-P^1 - Peter Scholze

Emmy Noether Lectures
Topic: Real local Langlands as geometric Langlands on the twistor-P^1
Speaker: Peter Scholze
Affiliation: Max-Planck-Institut für Mathematik, Bonn
Date: March 04, 2024
Sponsored by the Minerva Research Foundation.
In 2014, Fargues realized that one can formulate the local Langlands correspondence over p-adic fields as a geometric Langlands correspondence on the Fargues-Fontaine curve. This raises the question of a similar realization of the local Langlands correspondence over the real numbers. The goal of these lectures is to explain a possible formulation. As part of this, we will give a new perspective on the theory of variations of twistor structure, a generalization of the theory of variations of Hodge structure. This uses the theory of analytic stacks developed in our joint work with Clausen, of which we will give a brief overview.