Compactifications of (locally) symmetric spaces and ideal Poisson Voronoi tesselationsMPIM

by Anna Wienhard (MPI Leipzig)

Thursday May 28, 2026, 1:30 PM → 3:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Oberseminar Differentialgeometrie

The Poisson--Voronoi percolation model can be defined on any metric measured space as follows. 

Sample a random discrete set of points according to a Poisson point process of intensity $\lambda>0$, divide the space into the corresponding

Voronoi cells, color the cells black independently with probability $p\in(0,1)$ and consider the union of black cells. This model has been widely studied in Euclidean space and also beyond, notably in the hyperbolic plane by Benjamini and Schramm (2001). In this talk, we will discuss a new phenomenon for higher rank symmetric spaces. We will show an application of this result to a question of Hutchcroft and Pete (2020) and Pete and Rokob (2025), and its close connection to Gaboriau's fixed price problem. In the final part of the talk, we will explain the strategy of proof and in particular the way in which our approach builds on recent results about ideal Poisson--Voronoi tessellations and a breakthrough of Frączyk, Mellick and Wilkens (2025). Based on joint works with Jan Grebík and with Matteo D'Achille, Jan Grebík, Ali Khezeli, Amanda Wilkens.