[Mini-course]: Metric geometry on the configuration space | Professor Kohei Suzuki, Durham University
Title: Metric geometry on the configuration space
Speaker: Professor Kohei Suzuki, Durham University
Abstract: The configuration space Y(X) over a base space X is the space of all Radon point measures on X. The space Y(X) has been studied in many fields such as algebraic geometry (e.g., the hyperplane arrangement with X=Grassmannian), algebraic topology (e.g., the braid group with X=Euclidean plane), representation theory (e.g., the L^2-representation of diffeomorphism groups on manifolds X), statistical physics (e.g., interacting particle diffusions with X=Euclidean space). In this series of lectures, I will focus on the metric geometry of Y(X) induced by the 2-Wasserstein distance. As Y(X) does not support the volume doubling property, the established theory of PI spaces does not apply. The goal of the series is to elaborate on
- Metric geometry on Y(X);
- Curvature analysis on Y(X);
- Applications to infinite particle diffusion processes (including e.g. infinite particle Dyson Brownian motion);
- Open questions.
*After registering, you will receive a confirmation email containing information about joining the meeting.