The 13th Brauer Group Meeting

该奖项支持参加将于2018年6月18日至22日星期一至星期五在科罗拉多州立大学山校区举行的第13届布劳尔集团会议。会议的目的是聚集数学家的研究重点是布劳尔集团和相关领域。会议将包括高级和初级研究人员的演讲以及合作的时间和空间。组织者将尽最大努力确保会议参与者代表数学界的不同领域。这次会议的资金将用于支付会议设施和初级与会者的旅费。布劳尔小组是一个"小组"在数学意义上和研究人员从许多领域的数学，包括代数，数论，代数几何和拓扑学有相关的利益，了解对象，这组parametrizes。 低维几何学家研究所谓的特征变种及其衍生模式的组件上的Brauer类的存在性，以识别结补的属性。古典代数学家研究布劳尔群在其作用作为一个目录的司代数在一个领域。有许多开放和困难的问题，在这个经典的看法布劳尔集团;是所有部门代数的素数度循环？存在素指数的非交叉积除代数吗？度除n的循环代数类生成n-扭子群吗？代数几何学家研究布劳尔群作为一个重要的不变量的计划所产生的étale上同调。这一观点可以追溯到20世纪60年代和格罗滕迪克，他提出的问题仍在积极研究中。第13届Brauer小组会议的主要目标是将这些观点汇集在一起，以便同事们可以分享涉及Brauer小组的各种形式的利益问题的见解。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

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.