Title: (Non-)trivial classes in the bounded cohomology of CAT(0) cube complexes

Abstract: Bounded cohomology is a “normed” relative of ordinary cohomology. Although the definitions are quite similar, the properties of ordinary and bounded cohomology differ a lot. In particular, the bounded cohomology of the free group is still completely unknown in degrees greater than 3. I will explain how the cup product yields an approach to compute higher degree classes for free and “almost” free groups. This is based on joint work with Clara Löh and Francesco Fournier-Facio. https://arxiv.org/abs/2209.05811