[Mini-course]: Metric geometry on the configuration space | Professor Kohei Suzuki, Durham University


Tuesday, August 29, 2023 - 10:00 to Friday, September 1, 2023 - 11:00


Onsite (see classroom below) + Zoom


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. 

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