Speaker: Amotz Oppenheim
(Tel-Aviv University):
Title:
Iterations of quadratic polynomial functions over finite fields

Abstract:
I will present a recent result by Heath-Brown on the behavior of iterations of quadratic polynomials over finite fields. The result shows that the size of the image of (iterations of) a quadratic polynomial function, satisfying some natural conditions, has the  size predicted by a probabilistic argument.

This also gives some information on the size of cycles under quadratic maps.