##### Department of Mathematics,

University of California San Diego

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### Food for Thought Seminar

## Wee Teck Gan

#### UCSD

## The unreasonable effectiveness of modular forms in arithmetic

##### Abstract:

How many times can a prime number be expressed as the sum of n squares? What is the asymptotic distribution of integer points on a family of ellipsoids $ax^2 + by^2 + cz^2 = n$ as $n$ tends to infinity? I will explain how modular forms can be used to address these questions and others.

### February 1, 2007

### 12:00 PM

### AP&M 7321

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