Title:

Real Clifford Algebras and Quadratic Forms over the field of two elements: Two Old Problems Become One.

Abstract:

Real Clifford algebras were introduced by the English mathematician and philosopher William Kingdon Clifford in 1878. They generalize complex numbers and quaternions and play an important role in many branches of mathematics. Classification of real Clifford algebras was obtained by Chevalley in 1954: every real Clifford algebra is isomorphic to one of the algebras of real, complex, or quaternionic matrices whose size is a power of 2, or their double copies. Classification of quadratic forms over the field of two elements was solved by Dickson in 1900. The goal of this talk is to explain that these classification problems are equivalent.