Groups and Operator Algebras seminar: Avraham-Reem
Title: Conservativity and Dissipativity in Nonsingular Group Actions
Speaker: Nachi Avraham Re'em (Chalmers, personal website https://www.nachi.co.il/ )
Abstract: The general theory of nonsingular transformations or flows (also described as measure-class preserving or quasi-invariant) distinguishes recurrence behavior from transience behavior through the complementary notions of conservativity and dissipativity. For instance, the classical Poincaré Recurrence Theorem asserts that every probability-preserving transformation is conservative. A few classical results by Hopf, Halmos, Krengel, Maharam, and others characterize conservativity and dissipativity in various ways, including a structure theorem for dissipative transformations (Hopf) and dissipative flows (Krengel).
In this talk, I will show how this theory extends when generalized to nonsingular actions of locally compact second countable groups. Using a descriptive set-theoretic point of view, we develop a complete structure theorem for dissipative group actions. The talk is based on a joint work with George Peterzil.