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 |