[ Fall 2000] Wichita State University
Abstract:
Mandelbrot popularized the idea that fractals can offer a more realistic geometric view of nature by examining
fractal structures such as coastlines, trees and blood vessels. A large body of research has been built around
describing the geometric properties of fractals. But only within the last 15 years have mathematicians begun to
construct an analytic theory on fractals similar to modern analysis on manifolds. Until recently, the theory of
differential equations on fractal domains has focused on a narrow class of equations analogous to the Laplacian on
manifolds. In joint work with Robert Strichartz and Alexander Teplyaev at Cornell University, we examined a
much wider class of differential equations on the Sierpinski gasket. In this introductory talk I will present both the
basic notions behind analysis on fractals as well as some results obtained. The nature of this material allows a
complete presentation, so that students or faculty unfamiliar with research in either fractals or differential equations
can appreciate the combination of the two.
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Fall 2000]