Valeriya Kovaleva

University of Oxford

Isotropy of quadratic forms through random matrices

Linfoot Number Theory Seminar

13th November 2019, 11:00 am – 12:00 pm
Fry Building, 2.04

A quadratic form is called isotropic if it has a non-trivial zero over a certain ring. Suppose we want to compute the proportion of isotropic quadratic forms over integers. This proportion is a product of local proportions over the reals and the p-adic numbers, however these are very different worlds with completely different tools for solving the problem locally. I am going to talk about how to bring these different worlds together under the same framework, and solve the problem in a more universal way using the language of random matrices.

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