##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability and Statistics Seminar

## Rami Atar

#### Technion, Israel, University of Washington Visitor

## On the second Neumann eigenvalue

##### Abstract:

I will review results and open problems regarding simplicity of the lowest nonzero Neumann Laplacian eigenvalue on domains, and properties of the corresponding eigenfunctions related to the hot spots conjecture. I'll present a new simplicity result for a family of smooth planar domains, that is based on analysis of mirror couplings. Joint work with K. Burdzy.

### May 25, 2006

### 11:00 AM

### AP&M 5829

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