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Etale homotopy theory and the Hurwitz sums-of-squares problem
Fix a field F. As an outgrowth of his work on the existence of normed algebras, Hurwitz posed the problem of finding all dimensions in which a certain kind of "sum-of-squares" formula can exist over F. This problem remains open today. Until recently most known results applied only to characteristic 0 fields, and involved algebraic topology in an essential way. I will talk about how the methods of etale homotopy theory can be used to yield similar results in characteristic p, as well as some natural questions in motivic homotopy theory which arise out of this work.
Thursday, January 22, 2004, 245 Altgeld Hall, 4:00 p.m.
Mathematics Colloquia homepage