# of the CRC 1442 Geometry: Deformations and Rigidity

**Thursday, 15 July 2021
at 16:15 as hybrid event
in lecture hall M1 an via Zoom**

# K-theory everywhere

# Speaker: Arthur Bartels

We will give a gentle introduction to K-theory and discuss its relevance in geometric topology and elsewhere.

# Relation to arithmetic cohomology theories

# Speaker: Thomas Nikolaus

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.