Bruce Reznick

Affiliation: University of Illinois, Urbana-Champaign

Email: reznick@math.uiuc.edu

Title Of Talk: Recent results in 19th century algebra

URL: http://www.math.uiuc.edu/~reznick/floridatalk.pdf

Abstract: The length of a form p of degree d is the minimum number of linear forms whose d-th powers sum to p. Two familiar theorems about quadratic forms is that the length cannot decrease if the base field is enlarged, and, in the real case, the Law of Inertia. We show that the length depends on the field when d > 2 in a non-trivial way and that the Law of Inertia holds for binary quartic forms, but fails for binary sextic forms. We will also present a mysterious identity involving quadratics taken to the 14-th power.

Last update made Mon May 25 17:15:07 EDT 2009.
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