Student Number Theory seminar

Tuesday, July 17, 2012 10:00 pm - 10:00 pm EDT (GMT -04:00)

Cassie Naymie, Pure Mathematics Department, University of Waterloo

"Lev's bounds for subsets containing no 3-APs (Part 1)"

Abstract: We say that $\{x,y,z\}$ forms a three term arithmetic
progression (or 3-AP) if $x+z=2y$.  For a finite abelian group $G$ we're
interested in finding the largest cardinality of all subsets $A\subseteq
G$ with $A$ containing no 3-APs.  We denote this cardinality by $D(G)$.
In this talk we will prove a result of Lev's showing how $D(G)$ can be
bounded above based on the structure of the group $G$.