Speaker: Slawek Solecki
Cornell University
Will give a Colloquium entitled:
Generic measure preserving transformations and Descriptive Set Theory
Abstract: One of the areas of interest to Descriptive Set Theory is dynamics of Polish groups, that is, groups carrying a group topology that is separable and completely metrizable. Such groups are not, in general, locally compact. Therefore, in studying their dynamics, classical methods relying on Haar measure are not available. These methods can sometimes be replaced by descriptive set theoretic tools. I will describe how the descriptive set theoretic point of view led to an answer to a question in Ergodic Theory. The question lies within a long-established theme, going back to the work of Halmos and Rokhlin, of investigating generic measure preserving transformations. The answer to the question rests on an analysis of unitary representations of a certain non-locally compact Polish group that can be viewed as an infinite dimensional torus.
Date: 11-13-2024
Time: 4:00 pm
Location: 231 Hayes Healy Bldg
Originally published at math.nd.edu.