Inverse Theory of Set Addition

Series
ACO Student Seminar
Time
Friday, September 27, 2013 - 1:05pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ernie Croot – School of Math, Georgia Tech – http://people.math.gatech.edu/~ecroot/
Organizer
Cristóbal Guzmán
If A is a set of n integers such that the sumset A+A = {a+b : a,b in A} has size 2n-1, then it turns out to be relatively easy to prove that A is an arithmetic progression {c, c+d, c+2d, c+3d, ..., c+(n-1)d}. But what if you only know something a bit weaker, say |A+A| < 10 n, say? Well, then there is a famous theorem due to G. Freiman that says that A is a "dense subset of a generalized arithmetic progression" (whatever that is -- you'll find out). Recently, this subject has been revolutionized by some remarkable results due to Tom Sanders. In this talk I will discuss what these are.