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区校区举行的第13届布劳尔小组会议。会议的目的是聚集研究重点放在布劳尔集团及其相关领域的数学家。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。主办方将尽最大努力确保会议参与者代表来自数学界的不同领域。这次会议的经费将用于支付初级与会者的会议设施和旅费。布劳尔群是数学意义上的一个“群”，来自包括代数、数论、代数几何和拓扑学在内的许多数学领域的研究人员都有相关的兴趣来了解这个群参数化为对象的对象。低维几何学研究所谓的字符种类及其分支模式的组成部分上的Brauer类的存在，以识别结补补语的属性。经典代数学家研究布劳尔群作为域上除法代数的目录的作用。在Brauer群的这一经典观点中，有许多开放和困难的问题；所有素数阶除代数都是循环的吗？是否存在素数指数的非交叉积除法代数？N-扭子群是由n次除n的循环代数类生成的吗？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。第13届布劳尔小组会议的主要目标是将这些观点结合在一起，以便同事们可以就涉及布劳尔小组的各种形式的感兴趣的问题分享见解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.