Harmonic functions on groups

The classic Liouville theorem states that any bounded harmonic function on Euclidean space is constant. The same holds for discretely harmonic functions on a lattice. But what happens when the Euclidean lattice is replaced by other graphs, in particular Cayley graphs of groups? We will survey old and new results on relations between geometric and algebraic properties of groups, harmonic functions and probability. Based on joint work with various subsets of Itai Benjamini, Ariel Yadin, Hugo Duminil-Copin, Gidi Amir and Maria Gerasimova.
Light refreshments will be served after the seminar.