PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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