Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, March 1, 2010

Schreiber 006, 12:15

Matthew Foreman

University of California, Irvine

Classifying the ergodic measure preserving transformations

Abstract: In 1932 von Neumann formulated the problem of classifying ergodic measure preserving transformations of [0,1]. In the nearly 80 years that have followed, there has been considerable positive progress on this problem; notably Ornstein's work using the Sinai-Kolmogorov invariant "entropy" to classify Bernoulli shifts and the theorem of von Neumann and Halmos classifying discrete spectrum transformations.

More recently language and techniques from Descriptive Set Theory have been adapted to prove "anti-classification" results that show, in a rigorous way, that no classification is possible. This lecture presents several of these results that are joint work with Benjy Weiss and with Dan Rudolph.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006