Random Tessellations in Hyperbolic Space - First Steps

Explore the fascinating world of random tessellations in hyperbolic space in this one-hour lecture by Daniel Hug. Delve into the classical topic of random tessellations in Euclidean space and their applications before examining the recent developments in spherical space. Discover a new dimension-dependent phenomenon arising from Poisson hyperplane tessellations in hyperbolic space. Investigate the k-volume of the k-skeleton induced by such tessellations within a geodesic ball of radius r and learn about the central limit theorem (CLT) in this context. Compare the contrasting results between fixed radius with increasing intensity and fixed intensity with increasing radius, highlighting the unique characteristics of hyperbolic space compared to Euclidean space. Gain insights from this joint work with Felix Herold and Christoph Thäle, presented at the Hausdorff Center for Mathematics.