Date & Time: Wednesday, August 06, 2008, 16:00-17:00.
Venue: Ramanujan Hall
Title: Sums of Squares and the "290-Theorem"
Speaker: Manjul Bhargava, Princeton University
Abstract: The famous "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four square numbers. That is, the quadratic form a2 + b2 + c2 + d2 "represents" all (positive) integers.
When does a general quadratic form represent all integers? When does it represent all odd integers? When does it represent all primes? We show how all these questions turn out to have very simple and surprising answers.