Upcoming MAMS Colloquium Series
Spring 2023
Friday 2/24— 3:15-4:15 pm at Yost 306
Title: Random Spherical Polytopes
Speaker: Florian Besau (Vienna Technical University)
Abstract: A classical topic in approximation theory is to (randomly) approximate a given convex body in Euclidean space.
We will take a look at some classical results on random polytope approximation and compare them with recent results where we consider the question in non-Euclidean spaces, in particular in spherical geometry.
We focus on asymptotic results on the expected volume and face-numbers of the random polytope as the number of generating points tends to infinity. In particular we will look at the case where the spherical random polytope is generated in a spherical wedge. Here we found some exciting new behavior that deviates from the Euclidean picture.
We will take a look at some classical results on random polytope approximation and compare them with recent results where we consider the question in non-Euclidean spaces, in particular in spherical geometry.
We focus on asymptotic results on the expected volume and face-numbers of the random polytope as the number of generating points tends to infinity. In particular we will look at the case where the spherical random polytope is generated in a spherical wedge. Here we found some exciting new behavior that deviates from the Euclidean picture.