##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Ben Andrews

#### Australia National University

## On the fundamental gap of a convex domain

##### Abstract:

\indent The eigenvalues of the Laplacian (or Laplacian with potential) on a smoothly bounded domain domain are very natural quantities, arising as the fundamental tones of a drum, the rates of decay of diffusions, and the energy levels of quantum systems. I will discuss some of the history relating to inequalities for low eigenvalues, leading up to the proof of a conjecture of Yau and van den Berg for the `fundamental gap' or excitation energy of a convex domain.

Host: Lei Ni

### February 24, 2011

### 3:00 PM

### AP&M 6402

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