Albion College Mathematics and Computer Science Colloquium


Title:Sums-of-Squares Formulas
Speaker:Daniel Isaksen
Assistant Professor
Department of Mathematics
Wayne State University
Detroit, MI

Abstract:Consider the polynomial identity

(x12 +x22 )(y12 + y22) = (x1y1 - x2y2)2+ (x1y2 + x2y1)2

This formula might be generalized as

(x12 + ... + xr2)(y12 + ... + ys2) = z12 + ... + zn2

where each zi  is "bilinear" in the x's and y's in the sense that it is a sum of monomials of the form c (xi yk).  These identities are relevant to questions about normed algebras, embeddings of topological spaces, and linear algebra.

We'll find a few examples of such identities, but the problem of finding this type of identity is extremely difficult.  It turns out to be easier to show that identities cannot exist under certain circumstances.

Location:Norris 109
Date:2/10/2005
Time:4:10 PM


@abstract{MCS:Colloquium:DanielIsaksen
AssistantProfessor
DepartmentofMathematics
WayneStateUniversity
DetroitMI:2005:2:10,
author  = "{Daniel Isaksen
Assistant Professor
Department of Mathematics
Wayne State University
Detroit, MI}",
title   = "{Sums-of-Squares Formulas}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month   = "{10 February}",
year    = "{2005}"
}