Finite Fields and Model Theory

8 May 2008
11:00
Jamshid Derakhshan
Abstract
I will discuss some theorems of Chatzidakis, van den Dries, and Macintyre on definable sets over finite fields (Crelle 1992). This includes a geometric decomposition theorem for definable sets and a generalization of the Lang-Weil estimates, and uses model theory of finite and pseudo-finite fields. If time permits, I shall mention a recent application of this work by Emmanuel Kowalski on new bounds for exponential sums (Israel Journal of Math 2007). I would also like to mention some connections to the model theory of p-adic and motivic integrals and to general problems on counting and equidistribution of rational points.