Date:

Location:
745 Patterson Office Tower
Speaker(s) / Presenter(s):
John Hall
Title: Pairs of quadratic forms over padic fields
Abstract: The HasseMinkowski theorem implies that if a quadratic form over a number field k has a nontrivial zero over every achimedean and nonachimedean completion of k, then the form will have a nontrivial zero over k. It's natural to ask whether this is true for common nontrivial zeros of pairs of quadratic forms. In an effort to answer this question, new results about pairs of quadratic forms over padic fields have been proven. One such result, by HeathBrown, deals with finding forms in the pencil generated by a pair of quadratic forms over a padic field in 8 variables that split off 3 hyperbolic planes. In this talk, we will examine this result by HeathBrown, and we will discuss the ongoing effort of generalizing HeathBrown's hyperbolic plane result to pairs of quadratic forms over a padic field in an arbitrary number of variables.
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