##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Steve Zelditch

#### Northwestern University

## Solution of Kac's problem for analytic plane domains with a symmetry

##### Abstract:

Kac's `hear the shape of a drum" problem is the extent to which a plane domain is determined by its Dirichlet eigenvalues. I.e. is the map from domains to their spectra 1-1. We show that if the spectrum map is restricted to analytic plane domains with one up down symmetry (and an axis length fixed), then it is one-one. I.e. you can determine such a domain from its eigenvalues among other such domains. In joint work with Hamid Hezari, we also give a generalization to higher dimensions.

Host: Lei Ni

### April 15, 2010

### 4:00 PM

### AP&M 6402

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