For more information about this meeting, contact Svetlana Katok, Anatole Katok.

Title: | A new proof of Gromov's theorem on groups of polynomial growth |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Bruce Kleiner, Yale |

Abstract: |

In 1981 Gromov showed that any finitely generated
group of polynomial growth contains a finite index
nilpotent subgroup. This was a landmark paper in several
respects. The proof was based on the idea that one
can take a sequence of rescalings of an infinite group G,
pass to a limiting metric space, and apply deep results
about the structure of locally compact groups to draw
conclusions about the original group G. In the process,
the paper introduced Gromov-Hausdorff convergence,
initiated the subject of geometric group theory, and gave
the first application of the Montgomery-Zippin
solution to Hilbert's fifth problem (and subsequent
extensions due to Yamabe).
The purpose of the lecture is to give a new, much shorter, proof
of Gromov's theorem. The main step involves showing that any
infinite group of polynomial growth admits a finite dimensional
linear representation with infinite image. We establish this
using harmonic maps, thereby avoiding the Montgomery-Zippin-Yamabe
theory of locally compact groups which was used in Gromov's
original proof. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 04 / 28 / 2008 |

Time: | 03:35pm - 05:35pm |