Mathematics - Colloquium
Thursday, October 29, 2009
4:00 PM-5:00 PM
ABSTRACT: Most of my work over the past few years has been in analysis on post critically finite self-similar fractal sets. What makes these sets special is that one can sometimes define a Laplacian operator on them, and we can use this operator as the basic differential operator in an analytic theory. This opens up the possibility of studying physically interesting differential equations on these fractals.
A significant difficulty in this theory is that smoothness on these fractal sets is very different than it is on Euclidean spaces, so it is typically non trivial to get a handle on what smooth functions look like and to construct smooth functions with useful properties. This is where the self-similarity of the fractal can be an invaluable tool. I will describe a number of results in which self-similarity is exploited to construct or describe functions with useful properties, some of which are from papers I wrote with Bob Strichartz and various other coauthors. If time permits, I will speculate a little on the challenges that remain, particularly in producing a theory for more fractals that are more realistic models of physical objects.
Suggested Audiences: Adult, College
E-mail:
ma-chair@wpi.edu
Last Modified: October 23, 2009 at 3:52 PM
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