The ideal Poisson–Voronoi tessellation and some applications
Time and place
12:30–1:30 PM on Wednesday, April 1st, 2026; Marshak 1128
Amanda Wilkens (Carnegie Mellon University)
Abstract
Abstract: We explore some recent results involving a new random object, the ideal Poisson–Voronoi tessellation (IPVT), which inherently detects some of the geometry of its underlying space. In joint work with Fraczyk and Mellick, we use the IPVT to prove a deterministic result on the relationship between the volume of a manifold and the number of generators of its fundamental group. In joint work with D’Achille, Grebik, Khezeli, and Recke, we use the IPVT to prove a result on the uniqueness threshold in a related percolation model. In both cases, we use the IPVT’s wild behavior on spaces with a certain geometry (specifically, products of trees and symmetric spaces of higher rank semisimple Lie groups), originally discovered via a dynamical argument. We discuss this behavior and give some intuition for the main results.
