Metric functional boundaries of groups

In this talk I will introduce the concept of a "metric-functional". The notion goes back to works of Busemann and Gromov, but has been promoted by A. Karlson, among others.  These objects are meant to serve as a replacement for linear functionals in the general metric space setting, where there is no available linear structure.

In joint works with Bodart, Ron-George, and with Tointon, we studied metric functionals of metrics on (discrete) groups.

I will explain my main motivation, which is to find virtual homomorphisms, and how metric functionals arise naturally in this context.

No prior knowledge is required beyond basic math from undergraduate studies.