Combinatorial Algebraic Topology and Applications

L²-Betti number through triangle counting

speaker: Léo Bénard (Université de Aix-Marseille)

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.

timetable:
Mon 27 Nov, 14:30 - 15:30, Aula Dini
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