Ergodic Ramsey Theory: a Meeting Point of Combinatorics, Number Theory and Dynamics
by
Vitaly Bergelson
Ohi State University

Ergodic Ramsey Theory was born about 30 years ago when H. Furstenberg offered an ergodic-theoretical proof of the celebrated theorem of E. Szemeredi, namely, that any set of positive upper density in the natural numbers contains arbitrarily long arithmetic progressions. Furstenberg's ergodic approach has revealed the dynamic content of Szemeredi's theorem and has paved the way to numerous spectacular generalizations and extensions, most of which do not have as yet a conventional (i.e. non-ergodic) proof. We will discuss some of the recent developments including the Green-Tao theorem on arithmetic progressions in primes.

We shall conclude by formulating and discussing some natural open problems and conjectures.

Date received: March 27, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxa-27.