##### Department of Mathematics,

University of California San Diego

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### Food for Thought Seminar

## David Scheinker

#### UCSD, Graduate Student

## Fractal strings, hearing the sound of a drum, and the Riemann hypothesis

##### Abstract:

What do compact curves of infinite length, continuous, nowhere differentiable functions, and uncountable sets of measure zero have in common? It's not that they don't exist. The Koch Curve, the Weierstrass Function, and the Cantor Middle Thirds Set are all fractal sets and respective examples of each of the above. What do they have to do with Mark Kac's famous question: ``Can one hear the shape of a drum?" This talk is about how this question, Spectral Geometry, and Fractal sets come together in the work of Michel Lapidus and others to formulate a statement equivalent to the Riemann hypothesis. The talk will go roughly as follows: \\ 1. Pictures of fractals and a definition of non-integral, fractal, dimension. 2. A statement of the Riemann hypothesis. 3. ``One can hear the shape of a fractal string" if and only if the Riemann hypothesis holds. \\ The talk will involve mostly proofs by pictures and should be completely accessible.

### October 12, 2006

### 1:00 PM

### AP&M 7321

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