The 13th Brauer Group Meeting

University Of Montana, Missoula MT

Investigators

Abstract

This award supports participation in the 13th Brauer Group Meeting which will be held Monday - Friday, June 18 - 22, 2018 at the Mountain Campus of Colorado State University. The purpose of the meeting is to gather mathematicians whose research focuses on the Brauer Group and related areas. The conference will include talks given by both senior and junior researchers as well as time and space for collaboration. The organizers will do their best to ensure that the conference participants represent a diverse spectrum from across the mathematics community. Funds for this meeting will be used to pay for conference facilities and travel for junior participants. The Brauer Group is a "group" in the mathematical sense and researchers from many areas of mathematics, including algebra, number theory, algebraic geometry and topology have related interests in understanding the objects that this group parametrizes. Low dimensional geometers study the existence of Brauer classes on components of so-called character varieties and their ramification patterns to discern attributes of knot complements. Classical algebraists study the Brauer group in its role as a directory of division algebras over a field. There are many open and difficult questions in this classic view of the Brauer Group; are all division algebras of prime degree cyclic? Do there exist non-crossed product division algebras of prime exponent? Is the n-torsion subgroup generated by the classes of cyclic algebras of degree dividing n? Algebraic geometers study the Brauer group as an important invariant of a scheme arising from étale cohomology. This point of view goes back to the 1960's and Grothendieck, who suggested problems that are still actively being investigated. The primary goal of the 13th Brauer Group Meeting is to bring these perspectives together so that colleagues may share insights on problems of interest involving the Brauer group in its many forms. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.