The 10th Brauer Group Meeting

第十届布劳尔集团会议将于2012年8月6日至10日星期一至星期五在科罗拉多州立大学平利公园校区举行。该地点距离福特堡大约一小时车程。美国科林斯，科林斯Brauer群是一个抽象的代数群，由具有广泛兴趣的数学家研究。代数学家经常研究Brauer群的作用，它是域上除法代数的目录，最终目的是了解域中的算术复杂性。公开问题涉及描述的简单性、循环类的表达以及寻找域和代数群(如PGL(N))的合理的维度定义。代数几何学家将Brauer群作为上同调所产生的方案的一个重要不变量来研究。这种观点可以追溯到20世纪60年代的S和格罗森迪克，他们提出的问题仍在积极调查中。最近，布劳尔方案群和堆栈理论之间出现了深刻的联系，这些联系不仅被用来攻击一些长期悬而未决的问题，而且被用来启发新的问题和方法。这次会议的主要目标是将所有这些领域的知名和新手研究人员聚集在一起，就涉及布劳尔集团的各种形式的感兴趣的问题进行合作并分享见解。这次会议将有助于统一观点和多样化方法，不仅将在问题上取得进展和提高合作水平，而且还将启动新的研究人员进入布劳尔小组社区。正式演讲将由高级研究人员和年轻研究人员进行，包括研究生、博士后和年轻教职员工。还将分配时间进行非正式合作和公开问题会议，希望鼓励新的研究问题和合作。有关会议的信息以及演讲的标题和摘要将在http://www.math.uga.edu/$\sim$dkrashen/Brauer2012/上发布

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/