| DATE: | Thursday, October 5, 2000 |
| TIME: | 4:30 - 5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Robert S. Strichartz, Cornell |
| TITLE: | Music of the Fractals. |
How would a fractal object vibrate? In order to formulate this question mathematically, it is necessary to have an analog of the wave equation, and hence a notion of a Laplacian on a fractal. I will describe the theory developed by Jun Kigami that provides a constructive solution to this problem for a class of finitely ramified fractals which includes the familiar Sierpinski gasket. I will then described work that I and others have done to flesh in this theory, including how to do numerical analysis in this context, and I will give a detailed ``octave'' desription of the spectrum of the Sierpinski gasket. Lots of pictures; sorry, no sound effects. My expository article in the November 1999 Notices of the A.M.S. explains some of the ideas.