Polynomial Patterns in Subsets of the Integers

Combinatorics Seminar
Friday, September 30, 2011 - 3:00pm
1 hour (actually 50 minutes)
Skiles 005
University of Georgia
 How large can a subset of the first N natural numbers be before it is guaranteed to contain two distinct elements which differ by a perfect square? What if I replaced "perfect square" with the image of a more general polynomial, or perhaps "one less than a prime number"? We will discuss results of this flavor, including recent improvements and generalizations.