Discrete Ricci curvature and homology of graphs

11.06.2024 15:00 - 17:00

Florentin Münch (MPIM Leipzig)

In the first part, we give a general introduction on discrete Ricci curvature based on gradient estimates for the heat equation. As consequences of lower Ricci curvature bounds, we derive spectral gap estimates and diameter bounds, and we discuss rigidity.

In the second part, we show that the first Betti number of a natural cell complex associated to the graph is zero in case of positive curvature. Moreover, we give a bound on the first Betti number in case of non-negative curvature. We finally show that infinite graphs with non-negative curvature have at most two ends.


G. Arzhantseva, Ch. Cashen


SR 8, 2. OG, OMP 1