Monday, September 23, at 327 Yost
Talk: 1:30 - 2:30 p.m.
An elementary introduction to iterated function systems will be given. In particular, the two-dimensional Sierpinski gasket will be described. Two different ways of representing the Sierpinski gasket as a boundary of a Markov chain will be explained. One of these representations implies the so-called Poisson formula for the harmonic functions on the gasket where the harmonic functions are defined in terms of a mean-value property. I will also sketch how to extend this formula to a wider class of fractal sets and how to use this formula to develop a harmonic analysis on this type of fractals.