# Difference Sets and the Primes

 ARITHMETIC COMBINATORICS Topic: Difference Sets and the Primes Speaker: Tom Sanders Affiliation: University of Cambridge, UK and Member, School of Mathematics Date: Tuesday, October 2 Time/Room: 2:00pm - 3:00pm/S-101

We shall discuss joint work with I Z Ruzsa in which it is shown that if A is a subset of {1,..,N} such that its difference set contains no number of the form $p-1$ for $p$ a prime, then $|A|=O(N\exp(-c\sqrt{4}{\log N}))$ for some absolute $c>0$.