PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yakov Pesin, Sergei Tabachnikov.

Title:A big familly of algebras: quaternions, octonions and other cousins
Seminar:Department of Mathematics Colloquium
Speaker:Valentin Ovsienko, University of Lyon, France
Abstract:
"The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative." The citation from John Baez offers an excellent description of the familly. I will introduce other algebras-second-cousins and explain the main properties that characterize them (and distinguish from the other Cayley-Dickson algebras). As an application, I will talk of the celebrated Hurwitz problem on sums of squares and its relations to topology.

Room Reservation Information

Room Number:MB114
Date:10 / 27 / 2011
Time:04:00pm - 05:00pm