Mathematics Colloquiumm
Date and time: Thursday, 24 November 2022, 2.30 pm Venue: Ramanujan Hall Speaker: Parimala Raman, Emory University, Atlanta, GA, USA Title: Quadratic forms over function fields Abstract: A classical theorem of Hasse-Minkowski leads to the fact that every quadratic form in at least five variables over a totally imaginary number field represents zero nontrivially. One is naturally led to similar questions concerning function fields of curves over totally imaginary number fields. Do quadratic forms in a sufficiently large number of variables represent zero nontrivially over these fields? This is a big open question even for the rational function field in one variable over a totally imaginary number field. The expectation is that every quadratic form in at least nine variables over such a field represents zero nontrivially; over function fields of p-adic curves, every form in nine variables admits a nontrivial zero. We shall explain some recent progress in this direction.