Event Type:

Department Colloquium

Date/Time:

Friday, March 4, 2011 - 06:00

Guest Speaker:

Institution:

Hunter College and CUNY Graduate Center

Abstract:

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.