Linkage of quadratic Pfister forms

The algebraic theory of quadratic forms connects fascinating topics, from Hurwitz’ theorem and Hilbert’s 17th problem, to the theorems of Voevodsky-Orlov-Vishik and Voevodsky-Rost on the Witt ring and Milnor’s K-theory, and beyond.

After proving to the audience that this is a beautiful subject, I will try to explain why and how everything is harder in characteristic 2.

I will describe the effects of linkage of quadratic Pfister forms, in particularly in characteristic 2, where one has to distinguish between left- and right-linkage. I will describe a potential invariant (which fails), and construct sets of forms that should be linked, but aren't.