Conference: Cohomology and Support in Representation Theory and Related Topics

会议：表示论及相关主题中的上同调和支持

• 批准号: 1201345
• 负责人: Julia Pevtsova
• 金额: $ 4.05万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1201345&HistoricalAwards=false
• 关键词: Conference; Cohomology; Support; Representation; Theory

A workshop on "Cohomology and Support in Representation Theory and Related Topics" will be held at the University of Washington, Seattle, on August 1 - 5, 2012. Following seminal work of Daniel Quillen, cohomological support varieties have been studied and seen numerous applications to the development of the representation theory of a wide array of structures: finite groups, Lie algebras (and superalgebras), finite group schemes, Hopf algebras, small quantum groups, and general self-injective algebras. In recent years, there has been tremendous progress in unifying the theories for different structures. Further, the notion of "support" itself has evolved considerably from its initial definition in terms of the cohomology of a finite group to a much more category theoretic concept. The workshop "Cohomology and Support in Representation Theory and Related Topics," following on the footsteps of the summer school on the same topic, will be an opportunity to summarize the history of this theoretical tool, to report on recent progress on multiple fronts, and to prepare a new cadre of mathematicians to continue the extensive development and applications of supports in many different areas of mathematics. Additional information on the workshop can be found at http://www.math.washington.edu/~pischool/The workshop "Cohomology and Support in Representation Theory and Related Topics" will bring mathematicians from different areas together to foster interaction and find new connections between multiple fields united by their use of the concept of "support" and will introduce a new generation of young researchers to the field. The organizers of the workshop are Christopher Bendel (University of Wisconsin-Stout), Henning Krause (Universitat Bielefeld), and Julia Pevtsova (University of Washington). There are twenty four confirmed/tentatively agreed speakers which include leading researchers in several different areas of representation theory, commutative algebra, and triangulated categories from around the world. The workshop will follow directly on the footsteps of a summer school for graduate students and recent PhDs to be held one week prior at the same location. The summer school will present three series of lectures introducing young mathematicians to several active directions of research within the broad field to be covered more deeply during the workshop. Such a juxtaposition will provide the junior participants with a valuable opportunity to take the foundational knowledge they acquire during the summer school and use it to delve into current problems during the workshop. Taken together, the summer school and the workshop are aimed to be both a thorough survey on the exciting recent developments in the field and the venue for an active discussion of future prospects and open problems.

2012年8月1日至5日，将在西雅图华盛顿大学举办“表征理论和相关主题中的上同源性和支持”研讨会。继Daniel Quillen的开创性工作之后，上同调支撑簇已经被研究并被广泛应用于一系列结构的表示理论的发展：有限群、李代数(和超代数)、有限群方案、Hopf代数、小量子群和一般自内射代数。近年来，在统一不同结构的理论方面取得了巨大的进展。此外，“支持”的概念本身已经从最初用有限群的上同调来定义的概念演变成了一个更具范式论意义的概念。“表示理论和相关主题中的上同调和支持”研讨会将是一个机会，总结这一理论工具的历史，报告在多个方面的最新进展，并培养一支新的数学家队伍，继续在许多不同的数学领域广泛开发和应用支持。有关研讨会的更多信息可在http://www.math.washington.edu/~pischool/The研讨会上找到：“表示理论和相关主题中的上同调和支持”将把来自不同领域的数学家聚集在一起，促进互动，并找到通过使用“支持”概念联合起来的多个领域之间的新联系，并将向该领域引入新一代年轻研究人员。研讨会的组织者是克里斯托弗·本德尔(威斯康星大学-斯托特分校)、亨宁·克劳斯(比勒费尔德大学)和朱莉娅·佩夫索娃(华盛顿大学)。有24位确定/暂时同意的发言者，其中包括来自世界各地的几个不同领域的主要研究人员，包括表示理论、交换代数和三角范畴。研讨会将紧跟一周前在同一地点为研究生和新近博士举办的暑期学校的脚步。暑期班将提供三个系列的讲座，向年轻的数学家介绍在广泛的领域内几个活跃的研究方向，这些研究将在研讨会上更深入地讨论。这样的并列将为初级学员提供宝贵的机会，利用他们在暑期学校获得的基础知识，并在研讨会期间深入研究当前的问题。综上所述，暑期班和工作坊的目的既是对该领域令人兴奋的最新发展的全面调查，也是积极讨论未来前景和有待解决的问题的场所。