A Survey of Some Results Related to Roth's Theorem

Research Horizons Seminar
Wednesday, January 25, 2012 - 12:05
1 hour (actually 50 minutes)
Skiles 005
School of Mathematics, Georgia Tech
In this talk I will survey some recent results related to Roth's Theorem on three-term arithmetic progressions. The basic problem in this area is to determine the largest subset S of the integers in {1,...,n} containing no triple of the form x, x+d, x+2d. Roth showed back in the 1950's that the largest such set S has size o(n), and over the following decades his result has been considerably improved upon.