Colloquium: Dr. Stefan Gille (University of Alberta)

Dear All,

Here are the details regarding the next Math & Stats Colloquium:

Date / Time: Friday, February 9th @ 3:30 P.M.

Location: ARTS 101

Title: Sums of squares, composition algebras, and Pfister forms

Speaker: Dr. Stefan Gille (University of Alberta)

Abstract: Given two positive real numbers A and B which are sums of n squares, is their product C also a sum of n squares? This is clearly true, but what happens if one wants the squares making up C to depend linearly on the ones making up A and B? This is the so-called Hurewicz problem solved at the end of the 19th century, which led to the discovery and classification of composition algebras over the real numbers.

In the first part of my talk, I will discuss this problem and its solution using composition algebras. In particular I will define composition algebras and its norm form, which is a special quadratic form, a so called Pfister form. Pfister forms play a crucial role in the algebraic theory of quadratic forms and are also related to 'sums of squares problems' over arbitrary fields. This will be discussed in the second part of my talk.

Coffee / Tea / Treats: 2:45 P.M. in McLean 201 (Lounge)

Note for Grad Students: Attendance is mandatory for graduate students in Math & Stats. There will be a sign-in sheet at the talk.