I would like to invite you to the seminar lecture by Prof. Dr Daniel Hug Karlsruhe Institute of Technology:

Title: "Poisson processes of planes and Boolean models in hyperbolic space"

Abstract: Poisson processes of hyperplanes and the Boolean model are among the
best studied models in stochastic geometry. Until recently, however, these studies were
essentially restricted to Euclidean space. An investigation of the asymptotic fluctuations
of the k-skeleton of a Poisson process of hyperplanes in -dimensional hyperbolic
space H" exhibited first surprising phenomena. For instance, it turned out that
depending on the asymptotic scenario, asymptotic normality cannot always be
expected and in fact depends on the dimension of the space. We describe the current
state of our knowledge concerning the limiting behaviour of the volume of intersections
of Poisson k-planes in Id. Then we turn to Poisson particle processes and the Boolear
model in hyperbolic space and highlight recent findings, including results on exact and
asymptotic formulas for expectations and variances of geometric functionals and
central limit theorems. Also here, new phenomena arise compared to what we know
about Boolean models in Euclidean space.

Date: Tuesday 21.01.2025

Location: Room 220, Helmholtzstraße 18

Time 4:00 pm