Expanding representation in Noncommutative Algebra and Representation Theory: WINART2 Workshop

扩展非交换代数和表示论中的表示：WINART2 研讨会

• 批准号: 1900575
• 负责人: Chelsea Walton
• 金额: $ 1.14万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-02-01 至 2020-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1900575&HistoricalAwards=false
• 关键词: Expanding; representation; Noncommutative; Algebra; Representation

This award supports the participation of underrepresented minorities in the Women in Noncommutative Algebra and Representation Theory workshop (WINART2) at the University of Leeds on May 20 - 24, 2019. Noncommutative algebra and representation theory are two closely intertwined areas of research in Algebra that have strong ties to many other fields in mathematics and quantum physics such as conformal field theory, operator algebras, string theory, topological field theory, and the various guises of noncommutative geometry. Noncommutative algebra creates an algebraic framework for generalizing the study of polynomials to other rings that fail to be commutative, and representation theory is a powerful tool for investigating the action of an algebraic object on a space as linear operators and matrices. As in many areas of mathematics, women have been underrepresented in these areas of research. The goal of this workshop to bring together some of the best experts and junior participants working on these topics, particularly researchers from underrepresented groups, to collaborate on research projects. This workshop will be the second of its kind for these fields. Like the first WINART workshop (held at BIRS in March 2016), WINART2 will have a great impact on the research careers of those in attendance, and as a result, it will positively impact the research area as a whole. Funding will be prioritized for US-based junior participants.There will be eight research groups present at the workshop led by a pair of research leaders in Noncommutative Algebra and Representation Theory. Topics include: cluster categories; tensor invariants under Hopf algebra actions; algebraic, geometric, and categorical aspects of diagram algebras; Brauer and partition algebras; geometric models and representation theory; Burnside rings and Mackey functors for profinite groups; quantum symmetries- fusion categories and Hopf algebras; and Hochschild (co)homology, quivers and Gerstenhaber bracket. Further information can be found at the workshop website: http://women-in-ncalg-repthy.org/conferences/winart2-workshop-may-2019/.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.

该奖项支持代表性不足的少数群体参加 2019 年 5 月 20 日至 24 日在利兹大学举行的女性非交换代数和表示论研讨会 (WINART2)。非交换代数和表示论是代数研究中两个紧密相连的领域与数学和量子物理的许多其他领域有密切的联系，如共形场论、算子代数、弦论、拓扑场论、以及非交换几何的各种形式。非交换代数创建了一个代数框架，用于将多项式的研究推广到其他不能交换的环，而表示论是研究代数对象作为线性算子和矩阵在空间上的作用的强大工具。与许多数学领域一样，女性在这些研究领域的代表性不足。本次研讨会的目标是汇集研究这些主题的一些最优秀的专家和初级参与者，特别是来自代表性不足群体的研究人员，共同开展研究项目。本次研讨会将是这些领域的第二次此类研讨会。与第一届 WINART 研讨会（2016 年 3 月在 BIRS 举行）一样，WINART2 将对与会者的研究生涯产生巨大影响，从而对整个研究领域产生积极影响。资金将优先用于美国的初级参与者。将有八个研究小组出席研讨会，由两位非交换代数和表示论研究带头人领导。主题包括：集群类别； Hopf 代数作用下的张量不变量；图代数的代数、几何和分类方面；布劳尔和分区代数；几何模型和表示理论；有限群的 Burnside 环和 Mackey 函子；量子对称性-融合范畴和Hopf代数；和 Hochschild (co) 同源性、箭袋和 Gerstenhaber 括号。更多信息可在研讨会网站上找到：http://women-in-ncalg-repthy.org/conferences/winart2-workshop-may-2019/。该奖项反映了 NSF 的法定使命，经评估认为值得支持利用基金会的智力优势和更广泛的影响审查标准。