Branching in Planar Optimal Transport and Positive Definite Functions

Explore a 36-minute mathematics lecture that delves into the Gilbert-Steiner problem of optimal mass transport on a Euclidean plane, focusing on the relationship between two finitely supported probability distributions. Learn about groundbreaking research conducted with Danila Cherkashin demonstrating that branching points must have a degree of 3 when the cost of mass transfer per unit distance is proportional to m^p (0 < p < 1). Discover how the theory of positive definite functions connects to optimal transport theory in this presentation from St Petersburg State University researcher at the Institut des Hautes Etudes Scientifiques (IHES).