Probabilistic Methods in Geometry and Topology

Learn how probabilistic methods, originally developed for combinatorics, have evolved into powerful tools for proving cutting-edge theorems in algebra, Riemannian geometry, and algebraic topology in this mathematical lecture by Mikołaj Frączyk from Jagiellonian University. Discover how these techniques work by creating random models to demonstrate the existence of mathematical objects or structures with desired properties, rather than explicitly constructing them. Explore the transition from classical applications in graph theory and colorings to modern breakthrough applications across diverse mathematical fields. Review recent state-of-the-art applications that showcase how probabilistic reasoning has become instrumental in advancing our understanding of geometric and topological problems.