Event Detail

Event Type: 
Department Colloquium
Friday, March 4, 2011 - 06:00

Speaker Info

Hunter College and CUNY Graduate Center

A discrete dynamical system is a set S together with a
function f from the set S into itself. Considering the sequence of
all iterates f(x), f(f(x)), f(f(f(x))), etc., of the function f, one
is especially interested in the interaction of these iterates with
whatever mathematical structure the set S may possess. Arithmetic
dynamics could be described broadly as the study of discrete dynamical
systems on sets S of number-theoretic interest. For example, S could
be the field of rational numbers, and f could be a polynomial. More
generally, S could be an algebraic variety over a number field, or the
function field of a curve, or a p-adic field, or a finite field. In
this talk I will introduce the topic of arithmetic dynamics, I will
explore several explicit examples, I will discuss two open problems,
and I will report on partial progress on these problems.