Konstantin Slutsky : Approaches to the Gromov's theorem on groups of polynomial growth

Posted by , part of the Louise Hay Logic Seminar.

At

April 8, 2010, 3 p.m.

In

SEO 612

Abstract

The celebrated theorem of Gromov states that every group of polynomial growth is virtually nilpotent. Gromov's original approach used notion of a limit of metric spaces and had a strong flavor of model theory. It was later polished and further developed by van den Dries and Wilkie. They proved Gromov's theorem, and in fact a slightly more general version of it, using machinery from non-standard analysis. Both proofs had a "disadvantage": the heavy use of deep results by Montgomery and Zippin on the Hilbert's fifth problem. Recently a new proof, that avoids Montgomery-Zippin analysis, of Gromov's result was suggested by Bruce Kleiner. I'll try to give an overview of the ideas used in all the approaches above.

There will be tea to start and perhaps dinner afterward.