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Joint Mathematical seminar of Saint Petersburg State University and Peking University
June 30, 2020 15:00–16:00, St. Petersburg, online
 


Dynamics in the space of metrics and new invariants in ergodic theory

A. M. Vershik

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Video records:
MP4 146.0 Mb
Supplementary materials:
Adobe PDF 33.4 Kb
Adobe PDF 753.9 Kb

Number of views:
This page:308
Video files:50
Materials:47



Abstract: 1. Admissible metrics on the measure space: new trend in the theory of mm spaces.
2. Classification of mm-spaces. Matrix distributions.
3. Thе actions of measure preserving groups in the space of admissible metrics in measure space. ($\mathcal{M} \subset L^1(X\otimes X, \mu \otimes \mu)$).
4. Average metrics, ergodic limit and asymptotic invariants,
5. Sclaing entropy. Scaling entropy function. Examples.
6. Theorem. Bounded scaling entropy and discrete spectra. Sequential entropy by Kushnirenko. All possible scalings.
7. New geometrical problems.

Supplementary materials: bibliography.pdf (33.4 Kb) , dynamics_of_metrics_china.pdf (753.9 Kb)

Language: English

Website: https://english.math.pku.edu.cn/conferences/245.html
 
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