PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephen Simpson.

Title:Inverting the Furstenberg correspondence
Seminar:Logic Seminar
Speaker:Jeremy Avigad, Carnegie Mellon University
Abstract:
Roughly speaking, the Furstenberg correspondence principle shows that given any sequence of sets $S_n \subset \{0, \ldots, n-1\}$, there exists a subsequence and a shift-invariant measure $\mu$ on $2^\mathbb{N}$ which reflects the limits of the densities with which patterns occur in that subsequence. I will explain how this process can be inverted, so that any shift-invariant measure $\mu$ on $2^\mathbb{N}$ (not necessarily ergodic) can be represented by such a subsequence. Similarly, factors of $\mu$ can be represented as limits of appropriate ``factors'' of the elements of this subsequence. More generally, I will discuss some of the relationships between ergodic-theoretic and finite fourier-analytic methods in ergodic Ramsey theory that play a key role in work by Tao.

Room Reservation Information

Room Number:MB315
Date:11 / 16 / 2010
Time:02:30pm - 03:45pm