Green series of walks on groups

par Corentin Bodart (University of Oxford)

vendredi 4 avr. 2025, 10:30 → 11:30 Europe/Paris

E2 1180 (Tours)

I will start by defining the Green series of Cayley graphs, and describe previous methods used to prove positive and negative results regarding their algebraic properties. These usually rely on links with the Word Problem and analysis of the random walk on these graphs. I'll explain a new result providing the first example of a virtually nilpotent group with non D-finite Green series. Some key tools are a lattice path model for elements of the Heisenberg group, a lemma of Garrabrant and Pak, as well as a good dose of number theory.