Mini-courses
2022 Mini-course I
Title: Curvature and Optimal transport
Speaker: Professor Asuka Takatsu, Tokyo Metropolitan University
In this series of lectures, I first review the notion of curvature (Gaussian curvature and Ricci curvature).
In particular, I recall some comparison theorems (Toponogov's triangle comparison theorem, Bishop--Gromov volume comparison theorem etc).Then I introduce a generalized notion of curvature in non-smooth spaces.
March 8, 2022 10:00 - 11:00 AM
March 9, 2022 10:00 - 11:00 AM
March 10, 2022 9:30 - 10:30 AM
2022 Mini-course II
Title: A brief introduction to branched optimal transport
Speaker: Professor Jun Kitagawa, Michigan State University
The optimal transport (also known as Monge-Kantorovich) problem is a classical optimization problem which has recently become the focus of much research with connections to various fields such as PDEs, geometry, and applications. In particular, it provides an effective way to metrize the space of probability measures on a given metric space. However, there is an alternate approach to metrizing such spaces using so called branched optimal transport. Branched optimal transport is based on the classical Gilbert-Steiner problem, later adapted by Qinglan Xia, and in contrast to the Monge-Kantorovich approach tends to yield branching structures. In this series of lectures I will introduce the basics of branched optimal transport and discuss some of the known results in the literature.