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Graduate Pizza Seminar

Fractals! Fra ls! F a l !

Karuna Sangam - Rutgers University

Location:  GSL - Hill 701
Date & time: Friday, 04 October 2019 at 1:40PM - 2:40PM


Fractals: what are they? The answer to that question could probably take an entire pizza seminar talk on its own, but we aren't going to bother ourselves too much about that. Instead, we're going to focus on trying to make analysis work on a class of fractals called post-critically finite (PCF) fractals -- a famous example of which is the Sierpinski gasket. One might wonder how it is even possible to do analysis on a fractal, given that they do not have the nice properties of smoothness that we often prefer when doing analysis. As it turns out, it's possible to define a Laplacian operator on a PCF fractal by taking graph approximations (for all you combinatorialists out there). In this talk, I'll define the Laplacian and gradient on a Sierpinski gasket, and discuss some results I helped prove for a generalized n-dimensional gasket.

If we have additional time, I will completely switch gears and talk about the homeomorphism group of the Sierpinski carpet, a similarly named but very different fractal on which I won't be doing analysis.

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