#### Conference abstracts

Session A4 - Computational Geometry and Topology

July 12, 16:00 ~ 16:25 - Room B7

## Maximally persistent cycles in random geometric simplicial complexes

### Matthew Kahle

### Ohio State University, United States - mkahle@math.osu.edu

One motivation for the emerging subject of stochastic topology is as a null hypothesis for topological statistics. There has been some earlier work studying the topology of random geometric simplicial complexes, but until recently not much was known about persistent homology of these complexes

In joint work with Omer Bobrowski and Primoz Skraba, we prove upper and lower bounds on the persistence of the maximally persistent cycle, agreeing up to a constant factor. The results hold for persistent $k$-cycles in $\mathbb{R}^d$, for all $d \ge 2$ and $2 \le k \le d-1$, and for both Vietorisâ€“Rips and Cech filtrations. This is an important step in the direction of quantifying topological inference, separating topological signal from noise.

Joint work with Omer Bobrowski (Technion, Israel) and Primoz Skraba (Jozef Stefan Institute, Slovenia).