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.

Lecture 1 | August 29, 2023  10:00 - 11:00 　　　【L4E01】

Lecture 2 | August 30, 2023  10:00 - 11:00 　　【L4E01】

Lecture 3 | August 31, 2023  10:00 - 11:00 　 【L4F01】

Lecture 4 | September 1, 2023 10:00 - 11:00  　【L3B700】

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This lecture be accessible to senior math undergraduate and anyone above the level.