Working Seminar in Groups, Dynamics, and Operator Algebras

Date: February 21, 2020

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Konrad Wrobel, Texas A&M University

Title: Ornstein Theory I: Bernoulli Shifts and the Rokhlin Lemma

Abstract: Ornstein theory is a collection of techniques used to prove the Orstein Isomorphism Theorem, a beautiful and deep result which gives a complete classification of Bernoulli shifts by their entropy. Bernoulli shifts arise in many contexts including the theory of flows on manifolds, stochastic processes, transformations of the torus, symbolic coding, statistical mechanics, and ergodic theory. I'll introduce Bernoulli shifts and state the Kolmogorov-Ornstein Isomorphism Theorem. Then, I'll discuss a geometric representation of the Bernoulli shift in the form of the Rokhlin Lemma.