E 23

The (classical) u-invariant of a field F is the largest dimension of an anisotropic quadratic form defined over F. Very little is known in general about the connection between the u-invariant of F and the u-invariant of the corresponding rational function field F(t). We know how to compute, or even estimate, the u-invariant of F(t) only for some special fields F. I will briefly mention some of these examples and then focus on an example first constructed by J.-L. Colliot-Thelene and D. Madore. I will describe a way to simplify their work and at the same time strengthen their results. Definitions, background, and motivation will be provided and thus this talk should be accessible to graduate students and faculty members.

Prof. Dr. David Leep

University of Kentucky, Lexington, USA