Louise Hay Logic Seminar
Konstantin Slutsky
University of Illinois at Urbana-Champaign
Approaches to the Gromov's theorem on groups of polynomial growth
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.
Thursday April 8, 2010 at 3:00 PM in SEO 612