``Roth's Theorem, and the two dimensinonal generalization by Shkredov'' 

            M. Lacey, Georgia Tech.

ABSTRACT: Roth's theorem in Z_N states that a sufficiently
          dense subset A of Z_N has a non trivial arithmetic 
          progression. The proof of this result is very beautiful, 
          and still non trivial, in the finite field setting. 
          I review that, and then move to the two dimensional
          generalization of Roth's method of proof discovered 
          by Shkredov.
          There are many interesting sidelines of this, with
          important contributions by several people that I'll 
          mention in the talk.