Non-associative division algebras and projective geometry

Mathematical Conversations
Topic:Non-associative division algebras and projective geometry
Speaker:Charles Weibel
Affiliation:Rutgers University; Member, School of Mathematics
Date:Wednesday, February 26
Time/Room:6:00pm - 7:00pm/Dilworth Room

Projective planes satisfying certain symmetry conditions correspond to non-associative division algebras, by the work of Hilbert, Dickson, Albert, Wedderburn and Veblen. Knuth began the attempt to classify them over finite fields, and very few examples are known. I will relate relate this to an elementary problem in linear subspaces of matrix algebras, and show how some families are classified by etale cohomology. About Mathematical Conversations: We meet in Harry's Bar at 6pm, where free drinks are provided. After 20 minutes, we move to the Dilworth room, where the speaker gives a 20-minute talk, followed by 15 minutes of discussion with the audience. After that we return to the bar for further discussions. Website: http://www.math.ias.edu/~nicks/conversations.html