Collaborative Research: Conference on Geometric Methods in Representation Theory 2018 and 2019

协作研究：2018年和2019年表示论中的几何方法会议

• 批准号: 1839720
• 负责人: Ryan Kinser
• 金额: $ 1.18万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1839720&HistoricalAwards=false
• 关键词: Collaborative; Research; Conference; Geometric; Methods

The sixth and seventh conferences on Geometric Methods in Representation Theory will be held at the University of Iowa on November 17-19, 2018, and at the University of Missouri on November 23-25, 2019. Representation theory is a branch of modern algebra studying symmetries in linear spaces. It interacts with many other areas in mathematics, mathematical physics, and theoretical computer science. Geometric methods have become more and more fundamental in all of these areas. One of the main objectives of these conferences is to introduce beginning researchers in representation theory to the power of geometric methods. Keynote lectures for these conferences will be Milen Yakimov in 2018 and Lidia Angeleri Hugel in 2019. Each keynote lecturer will give two one-hour lectures, emphasizing geometric methods; these talks will be accessible to graduate students and postdoctoral researchers. There will also be several expository lectures given by other established researchers. The remainder of the lectures will be research talks given by other participants. These will include talks by graduate students and postdoctoral researchers related to their Ph.D. theses. The conference will provide an inviting atmosphere in which new collaborations can be formed and young researchers will have the opportunity to learn about cutting-edge geometric methods in representation theory. Moreover, the conference will enable early-career representation theorists to present their work and interact with the broader research community. Over the last 40 years, the representation theory of finite dimensional algebras has enjoyed a great impact of methods from algebraic geometry, in particular from geometric invariant theory and transformation groups. At the same time, this influence has led to the feedback of ideas and techniques from representation theory to geometry. One of the goals of the conferences on Geometric Methods in Representation Theory is to help strengthen and advance this interaction between geometry and representation theory. The topics of these conferences will include: quantum nilpotent algebras and quantum cluster algebras; Poisson geometry and quantizations of coordinate rings of varieties; tilting and silting theory; semi-invariants for bound quivers; geometric aspects of cluster algebras; degenerations of modules and the geometry of orbit closures in module varieties; moduli problems for finite dimensional algebras; and universal deformation rings and their connection to moduli spaces. More information about these conferences on Geometric Methods in Representation Theory at the University of Iowa and at the University of Missouri-Columbia can be found at http://homepage.math.uiowa.edu/~fbleher/CGMRT.html.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.

第六届和第七届表示论几何方法会议将于2018年11月17-19日在爱荷华大学、2019年11月23-25日在密苏里大学举行。表示论是现代代数研究的一个分支线性空间中的对称性。它与数学、数学物理和理论计算机科学的许多其他领域相互作用。几何方法在所有这些领域中变得越来越重要。这些会议的主要目标之一是向表示论的初级研究人员介绍几何方法的力量。这些会议的主题演讲分别是2018年的Milen Yakimov和2019年的Lidia Angeleri Hugel。每位主讲讲师将进行两次一小时的讲座，强调几何方法；这些讲座将向研究生和博士后研究人员开放。其他知名研究人员还将进行一些说明性讲座。其余的讲座将是其他参与者的研究报告。其中将包括研究生和博士后研究人员与其博士学位相关的演讲。论文。会议将营造一种温馨的氛围，促进新的合作，年轻的研究人员将有机会了解表示理论中的前沿几何方法。此外，该会议将使早期职业代表理论家能够展示他们的工作并与更广泛的研究界互动。在过去的40年里，有限维代数的表示论受到了代数几何方法的巨大影响，特别是几何不变量理论和变换群的影响。同时，这种影响导致了从表示论到几何的思想和技术的反馈。表示论中的几何方法会议的目标之一是帮助加强和推进几何与表示论之间的相互作用。这些会议的主题将包括：量子幂零代数和量子簇代数；泊松几何和簇坐标环的量子化；倾斜和淤积理论；绑定箭袋的半不变量；簇代数的几何方面；模块的退化和模块品种中轨道闭合的几何形状；有限维代数的模问题；和通用变形环及其与模空间的连接。有关爱荷华大学和密苏里大学哥伦比亚分校的表示论几何方法会议的更多信息，请访问 http://homepage.math.uiowa.edu/~fbleher/CGMRT.html。该奖项反映了通过使用基金会的智力价值和更广泛的影响审查标准进行评估，NSF 的法定使命被认为值得支持。