Wichita State University
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]