p-Adic Analogues of the Mandelbrot Set

By Jacqueline Anderson

September 11, 2012

Abstract

The Mandelbrot set is known for its fractal structure and has inspired much research in complex dynamics (and many pretty posters for mathematical events). Its p-adic analogue, however, is boring as can be - it is simply the unit disk. But, if you generalize this concept to higher degree polynomials, interesting objects emerge. I will discuss some background in complex and p-adic dynamics, and explain a result or two of mine. (I won't assume you know what p-adic numbers are, but you'll probably get more out of the talk if you do.)