Wednesday, October 16, 2019 - 14:00 in V3-201
Configuration Spaces Over Metric Measure Spaces
A talk in the Bielefeld Stochastic Afternoon series by
Kohei Suzuki from Scuola Normale Superiore di Pisa
| Abstract: |
The aim of this talk is to explore foundations of infinite-dimensional analysis and geometry on configuration spaces over non-smooth spaces. One of the main results is the complete identification of analytic and geometric structures on configuration spaces with the Poisson measure over diffusion metric measure spaces: the analytic structure is the diffusion structure generated by the square-field operator lifted from the base space; the geometric structure is the extended metric measure space induced by the $L^2$-transportation distance. As an application, curvature properties of configuration spaces over diffusion metric measure spaces are established. Another application is the stability of Cheeger energies and Brownian motions on configuration spaces under the measured Gromov convergence of base spaces. This is a joint work with Lorenzo Dello Schiavo from Bonn.
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