Texas A&M
University, Department of
Mathematics, 216 Milner Hall, 1st and 8th of October 2008, 3:00-3:50
Groups and Dynamics Seminar
Weak mixing and Property T
David Kerr of Texas
A&M
University
It is typically a hopeless task to try to classify dynamical systems up
to conjugacy. On the other hand, one can often isolate properties
which hold for generic systems in the sense of Baire category. I will
discuss the prevalence of different types of mixing behaviour and
how this is connected to the structure of the acting group, with
a focus on weak mixing and Kazhdan's property T. I will
also indicate how results in this direction relate to the
dichotomy between weak mixing and compactness as expressed by
the Furstenberg-Zimmer structure theorem.