Harmonic functions and boundaries

Baby NCG Seminar by Andreas Midjord

Title: Harmonic functions and boundaries

Abstract: After a short motivational introduction to classical harmonic analysis, we will direct our attention to the setup of a second countable, locally compact group G equipped with a Borel probability measure. In this setting, we define the notion of a harmonic function and observe their relations to random walks and G-spaces. From there on, we discuss the notion of a boundary and in particular the Poisson-boundary, which is inspired by the Dirichlet boundary problem. Finally, we discuss an application of boundary theory in relation to amenability of groups.