Orateur: Eiichi
Piguet
Titre: Quaternions and
sums of squares
Résumé:
The aim of this talk is to give an ingenious application of
quaternions by proving Lagrange's four square theorem (every natural number
can be represented as a sum of four integer squares). We will start by a
general definition of the ring of quaternions and we will put a quadratic
form on it. After examining the basic results, we will see the definition of
Hurwitz’s ring, which is the main object of the proof.