# Meeting Details

Title: Inverting the Furstenberg correspondence Logic Seminar Jeremy Avigad, Carnegie Mellon University 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.