The course is given by Francesco Fournier Facio and the problem sessions are led by Elena Bogliolo.

Abstract:

Bounded cohomology is a functional-analytic analogue of singular cohomology, with many applications in geometric topology and rigidity theory. Unfortunately, it is very hard to compute, most of all because there is no Mayer-Vietoris sequence. The last few years have seen major advances, with new computations especially in the realm of transformation groups, with applications to characteristic classes of bundles and Milnor-Wood inequalities.

In this minicourse I will survey the basic theory of bounded cohomology, the foundational results and the main applications, and then focus on these recent advances. The ultimate goal is to sketch the proof of the bounded acyclicity of the group of homeomorphisms of R^n, which uses essentially all tools currently at our disposal to compute bounded cohomology.