Shimura Varieties and Categorical LanglandsLecture

by Dr David Linus Hamann

Wednesday Nov 4, 2026, 8:30 AM → 9:15 AM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

The Langlands program predicts that the point counts of solutions to polynomial equations modulo a prime number p should be describable in terms of the Fourier analysis of certain very symmetric functions. At the heart of this program lie certain algebraic "Shimura varieties", whose cohomology sees the two sides of this striking correspondence. In this talk, we will introduce some aspects of the study of these varieties and their cohomology in the context of the Langlands program, and explain how, using a p-adic analogue of Hodge theory, they can be related to the study of moduli spaces of vector bundles on the "Fargues-Fontaine curve". This connection allows the use of powerful tools in the geometric Langlands program to be employed in the study of these objects. We will then conclude by illustrating some of the consequences in this perspective, discussing how certain objects in the geometric Langlands program; namely, "geometric Eisenstein functors" can be used to yield new consequences for the cohomology of these varieties.