Cornell Math - MATH 613, Fall 2000

MATH 613 — Fall 2000
Topics in Analysis: Analysis on Fractals

Instructor: Robert Strichartz
Final Time: MWF 10:10-11:00

Prerequisite: Math 611

Texts:

  1. Falconer, Fractal Geometry
  2. Kigami, Analysis on Fractals (xerox)

The first part of the course will cover standard material about fractals using Falconer's book, including Hausdorff and box dimension, iterated function systems, self-similar measures, dimensions of measures, multifractal formalism.

The second part of the course will cover the theory of "fractal differential equations." Since fractals are not manifolds, there is no standard theory of differential operators on fractals. Nevertheless, Kigami has constructed the analog of the Laplacian on a limited class of fractals, including the familiar Sierpinski gasket. We will describe this construction and discuss recent research in this area. To get an idea of the subject, see my expository article in the November 1999 issue of Notices of the AMS.