The aim of the summer school is to provide an introduction to recent advances in the understanding of the number-theoretic content of the cohomology of arithmetic groups and of algebraic K-groups of number rings. Uncovering this information reveals deep connections with algebraic geometry, namely with the theory of motives and with motivic homotopy theory. Surprisingly, this happens even when the arithmetic groups under consideration are not directly linked with algebraic varieties.

The mini-courses will cover the following topics:

Approaches to Harder's conjecture on Eisenstein congruences

Mixed Tate motives, Dedekind zeta values, and polylogarithms

Weighted cohomology of Shimura varieties

Motives and Hermitian K-theory of number rings

Motivic cohomology and the cohomology of arithmetic groups