Colorado State University
Ergodic Theory and the Properties of Large Sets
By Vitaly Bergelsohn
From Department of Mathematics
The Ohio State University, Columbus, OH
When March 23, 2006
11:00 am
Where Engineering E206
Abstract Many familiar theorems in various areas of mathematics have the following common feature: if A is a large set, then the set of its differences, A-A, is VERY large. For example:

(i) If A is a set of reals having positive Lebesgue measure, then there exists a positive real a, so that A-A contains the interval (-a,a).

(ii) If A is a set of natural numbers having positive upper density, then for any polynomial p(n) having integer coefficients and zero constant term, the set A-A contains infinitely many integers of the form p(n).

(iii) If F is an infinite algebraic field and G is a subgroup of finite index in the multiplicative group F*, then G-G = F.

In this talk we shall discuss these and other similar results from the perspective of Ergodic Ramsey Theory. This discussion will lead us to new interesting results and conjectures. In particular we will see the foregoing as a special case of the appearance of rather arbitrary finite configurations inside sufficiently large sets.

The talk is intended for a general audience.

Further Information Daniel Rudolph
There will be Refreshments in WB117 at 10.30am, preceeding the Colloquium.
The Colloquium counts as Seminar Credit for Mathematics Students.