# of the CRC 1442 Geometry: Deformations and Rigidity

**Thursday, 5 November 2020
at 16:15 via Zoom**

**Thursday, 5 November 2020
at 16:15 via Zoom**

The Langlands program explores a fruitful, but mysterious relation between natural objects of two seemingly unrelated areas of mathematics, namely arithmetic of varieties and harmonic analysis. It is manifested in equalities of L-functions. We explain the two areas and their L-functions and the general philosophy of the Langlands program.

In this talk I want to discuss geometric objects parametrizing representations of absolute Galois groups of global fields (like the rational numbers) and of local fields (like their p-adic completion). As part of the philosophy of the Langlands program the phenomena in the geometry of these so called moduli spaces of Galois representations are closely related to phenomena in the representation theory of the group GL_n (with various coefficients depending on the chosen moduli space of Galois representations). I will explain some geometric results, give examples of the interplay of geometry with representation theory and explain the relation of these results with the Langlands program and with some of the projects in the CRC.