Christian Rosendal, University of Maryland

The concept of amenability is ubiquitous in functional analysis, group theory and logic. In general, amenability of, for example, a group allows one to integrate bounded real valued functions on the group in a translation invariant manner, which is of great utility in many contexts. However, unbounded functions are a completely different matter. Nevertheless, by using tools from the theory of optimal transport, more specifically, optimal transportation cost spaces, we shall present a couple of results that show how one may integrate potentially unbounded Lipschitz functions defined on amenable groups as long as the latter admit no non-trivial homomorphism to $\mathbb R$. This is related to previous results of Schneider–Thom and Cuth–Doucha in the bounded setting. The talk will be aimed at a general mathematical audience.