The Distribution of Polynomials Over Finite Fields

COMPUTER SCIENCE/DISCRETE MATH II
Topic:The Distribution of Polynomials Over Finite Fields
Speaker:Tali Kaufman
Affiliation:Member, School of Mathematics
Date:Tuesday, April 1
Time/Room:10:30am - 12:30pm/S-101

I will present a recent result of Green and Tao showing the following. Let P:F^n --> F be a polynomial in n variables over F of degree at most d . We say that P is "equidistributed" if it takes on each of its |F| values close to equally often. We say that P has "low rank" if it can be expressed as a bounded combination of polynomials of lower degree, and "high rank" otherwise. The main result that I'll discuss: Let P be a polynomial of degree less than |F| . If P has high rank, then it is equidistributed.