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.

关于“表示理论中的上同调和支持及相关主题”的研讨会将于2012年8月1日至5日在西雅图的华盛顿大学举行。继丹尼尔·奎伦（Daniel Quillen）的开创性工作之后，上同调支撑变种已被研究，并在广泛结构的表示论的发展中得到了许多应用：有限群、李代数（和超代数）、有限群方案、霍普夫代数、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”的概念本身已经从有限群的上同调的初始定义发展到一个更加范畴论的概念。 研讨会“上同调和支持表示理论及相关主题”，在同一主题的暑期学校的脚步之后，将有机会总结这个理论工具的历史，报告多个方面的最新进展，并准备一个新的数学家骨干继续广泛的发展和支持在许多不同的数学领域的应用。 有关研讨会的更多信息可以在http://www.math.washington.edu/~pischool/The上找到研讨会“表示论和相关主题中的上同调和支持”将使来自不同领域的数学家聚集在一起，促进互动，并通过使用“支持”的概念来寻找多个领域之间的新联系，并将向该领域介绍新一代的年轻研究人员。 研讨会的组织者是Christopher Bendel（威斯康星大学斯托特分校）、Henning Krause（比勒费尔德大学）和Julia Pevtsova（华盛顿大学）。 有24个确认/暂时同意的发言者，其中包括来自世界各地的代表性理论，交换代数和三角分类的几个不同领域的领先研究人员。该研讨会将直接遵循一个暑期学校的脚步，为研究生和最近的博士将在同一地点举行一个星期前。 暑期学校将提出三个系列讲座介绍年轻的数学家在广泛的领域内的几个积极的研究方向将在研讨会期间更深入地覆盖。 这种并列将为初级参与者提供一个宝贵的机会，利用他们在暑期学校获得的基础知识，并在研讨会期间利用它来深入研究当前的问题。 总之，暑期学校和讲习班的目的是对该领域令人兴奋的最新发展进行全面调查，并积极讨论未来前景和开放问题。