The 10th Brauer Group Meeting

University Of Montana, Missoula MT

Investigators

Abstract

The 10th Brauer Group Meeting is a conference that will be held Monday - Friday, August 6 - August 10, 2012 at the Pingree Park campus of Colorado State University. This location is approximately one hour outside of Ft. Collins, CO, USA. The Brauer group is an abstract algebraic group studied by mathematicians with a wide variety of interests. Algebraists often study the Brauer group in its role as a directory of division algebras over a field, ultimately with the goal of understanding arithmetic complexity in fields. Open questions relate to simplicity of description, expression in terms of cyclic classes, and the search for a reasonable definition of dimension for fields and for algebraic groups such as PGL(n). Algebraic geometers study the Brauer group as an important invariant of a scheme arising from etale cohomology. This point of view goes back to the 1960's and Grothendieck, who suggested problems that are still actively being investigated. Recently deep connections have arisen between Brauer groups of schemes and stack theory, and these are being used not only to attack some longstanding open problems, but to serve as inspiration for new problems and approaches. The primary goal of this conference is to bring together established and beginning researchers from all of these perspectives to collaborate and share insights on problems of interest involving the Brauer group in its many forms. The conference will serve to both unify viewpoints and diversify methods, and will yield not only progress on problems and increased levels of collaboration, but the initiation of new researchers into the Brauer groups community. Formal talks will be given by senior level researchers as well as by young researchers, including graduate students, post-docs and young faculty. Time will also be allotted for informal collaboration and open problem sessions in hopes of encouraging new research questions and collaborations. Information about the conference and titles and abstracts for the talks will be posted at http://www.math.uga.edu/$\sim$dkrashen/Brauer2012/