#### Conference abstracts

Session A4 - Computational Geometry and Topology

July 10, 16:00 ~ 16:25

## Local Geometric Convergence of Embedded Graphs

### Benjamin Schweinhart

### Ohio State Unversity, United States - bschweinhart@gmail.com

We introduce a notion of local geometric convergence for embedded graphs in $\mathbb{R}^n$, developed in analogy with Benjamini-Schramm convergence of abstract graphs. It is defined in terms of weak convergence of probability measures on the space of embedded graphs with a smooth topology. We provide hypotheses under which it is implied by convergence of the first Wasserstein metric induced by the local Hausdorff distance. These concepts are used to state a universality conjecture for the long-term behavior of graphs evolving by curvature flow, and to test it computationally.