Title: Random polytopes: An introduction and recent developments
Speaker: Julian Grote (PhD Student, University of Bochum and Case Western Reserve University)
Abstract: Random polytopes are among the most classical and popular models considered in stochastic geometry, and their study has become a rapidly developing branch of mathematics at the borderline between geometry and probability. One reason for the increasing interest are the numerous connections and applications of random polytopes in other fields of mathematics, for example algorithmic geometry, convex geometric analysis, optimization or multivariate statistics.
In this talk I am going to start with an introduction into the theory of random polytopes; I explain how they are constructed and what has been done in the last decates. Moreover, I want to show how one can work with random polytopes by proving the famous ‘Efron-identity’. Then, the focus turns towards recent developments and I present different results that I recently obtained together with my supervisor Christoph Thäle. In particular, the powerful ‘method of cumulants’ that we used to derive our results will be explained in detail.