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 www.math.uga.edu/$sim$dkrashen/Brauer2012/
The award ``10th Brauer Group Meeting", number 1214939, was given for support of a mathematics conference held at the Pingree Park campus of Colorado State University. This meeting took place August 6-10, 2012. Its primary focus was the Brauer group in algebra and geometry. Participants were invited from around the US and abroad with an emphasis on young researchers and underrepresented groups. The Brauer group is a mathematical object of study with connections to many areas of mathematics. The topics presented in the Brauer group meetings traditionally focus on the algebraic aspects of the Brauer group including division algebras, algebras with involution, quadratic forms. Besides this, the conference also touched on algebraic geometry, cohomological Brauer groups and Brauer groups of schemes. The August 2012 meeting succeeded in its primary goal, which was to bring together both 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 served to both unify viewpoints and to diversify methods, and yielded not only progress on problems and increased levels of collaboration, but also the initiation of new researchers into the Brauer group community. To highlight one particular example, participants were fortunate to learn about some cutting edge connections being formed between algebra and topology using the Brauer group: David Saltman, a senior researcher in the field, proposed an open question to Benjamin Antieau about the existence of Azumaya maximal orders. In the fall following the conference Ben was able to answer this purely algebraic question in a joint work with Ben Williams, using techniques from algebraic topology, resulting in an article, which has been submitted for publication. Throughout the conference formal talks were given by senior level researchers as well as by young researchers, including graduate students, post-docs and young faculty. Time was also allotted for informal collaboration and open problem sessions in hopes of encouraging new research questions and collaborations. The conference had a website where all participants and talks were listed. The NSF award was used to provide room and board and also help with travel costs for participants. Of the 33 participants, 14 were young researchers, meaning they were still in graduate school or in a post-doctoral position. Nearly all of the young researchers gave talks at this meeting, allowing them the experience of giving a talk at a research conference and exposure to many senior level researchers in their field. In addition to attending talks during the days and evenings, nights and mornings had student and senior researchers alike discussing new ideas and working on collaborations.
