Student Analysis Seminar

Given two probability measures - and a notion of cost - how can I move one onto the other in the most efficient way possible? This is the motivating question of the field of optimal transport, but the field itself has connections to Riemannian geometry, Lagrangian mechanics, PDE, and many areas of applied math. We will discuss the history, motivation, and definitions of the field, before proceeding to more interesting topics. We will generally be light on proofs in an effort to present interesting results, which can be phrased and explained - if not proved - with more intuitive arguments. Time permitting, we will discuss ideas from (likely a strict subset of) the following range of topics: dynamic optimal transport, shortening principles, relationship to geometry, regularity and solvability issues for optimal transport, and the relationship to the Monge-Ampere equation. All that will be assumed is familiarity with measure theory. Speaker(s): Christopher Stith (University of Michigan)