27 nov 2023 -- 14:30
Abstract.
Given a compact manifold of dimension n with a triangulation, we define a combinatorial zeta function associated to random walks in the (n-1) skeleton of the triangulation. We show that this series extends as an analytic function on some disk, and recover a topological invariant, the first L2-Betti number, as its vanishing order at some point in the boundary of this disk.