Title: Counting polynomial configurations in dense subsets of the integers.

Abstract: Bergelson and Leibman proved that if p_1,...,p_k are integer
polynomials with zero constant term, then any dense subset of the integers
contains configurations of the form x,x+p_1(n),...,x+p_k(n). We show that
for "generic" (linearly independent) polynomials p_1,...,p_k, any dense
subset S of the integers contains "many" such configurations, at least as
many as when S is a random integer subset with the same density.
This is joint work with Bryna Kra.