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The Arithmetic of Quadratic Forms February 14, 2011 (04:10 PM PST - 05:10 PM PST)
Parent Program: --
Location: UC Berkeley, 60 Evans Hall
Speaker(s) Jonathan Hanke
Description Location : 60 evans Hall-  University of California-Berkeley

Speaker: Jon Hanke (University of Georgia)

The Arithmetic of Quadratic Forms

Quadratic forms with integer coefficients are among the oldest objects in mathematics
and lie at the crossroads between geometry and arithmetic. They have been studied by
mathematicians for thousands of years, but starting with the work of Gauss and
Legendre in the 1700s, new perspectives and techniques have been rapidly increasing
our understanding of the answers to classical questions like "What numbers can be
written as a sum of n squares?". We now know that there are deep connections
between these questions and many other interesting objects in mathematics (e.g.
modular forms, elliptic curves, abelian varieties, certain zeros of twists of the Riemann
zeta function). This talk will describe some of these ideas and techniques, explain what
questions they can be used to solve, and list some interesting problems that are still
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