Daqing Wan (UC Irvine).

Given a polynomial f(x) over a finite field F_q of q elements, we are interested in estimating the number of distinct values taken by f(x) as x runs over the finite field F_q. This problem has a long history, and has received increasing attentions in recent years. In this lecture, we try to give a comprehensive introduction to this topic and explain the various points of view (analytic, algebraic/group theoretic, geometric and algorithmic).