Speaker: Connor Cassady (University of Pennsylvania)
Title: Quadratic forms, local-global principles, and field invariants
Abstract: Given a quadratic form (homogeneous degree two polynomial) q over a field k, some basic questions one could ask are:
*Does q have a non-trivial zero (is q isotropic)?
*Which non-zero elements of k are represented by q?
*Does q represent all non-zero elements of k (is q universal)?
Over global fields F, the Hasse-Minkowski theorem, which is one of the first examples of a local-global principle, allows us to use answers to these questions over the completions of F to form answers to these
questions over F itself. In this talk, we'll explore when the local-global principle for isotropy holds over more general fields k, as well as connections between this local-global principle and universal quadratic forms over k.
Footnotes: We will be going for lunch and dinner with the speaker on Tuesday, January 31. If you are interested in coming for one of these events, please let Joshua know. (Just in case there is an algebraic geometry seminar prior to this, we will begin the talk 5-10 minutes late and then end the talk that much later. Smith Lab is across the street on West 18th, right past Scott lab. Room 1138 is on the left if you enter through the main entrance to Smith Lab.)
