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

第六届和第七届几何方法表示论会议将于2018年11月17日至19日在爱荷华州大学举行，并于2019年11月23日至25日在密苏里州大学举行。表示论是现代代数的一个分支，研究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中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基本。这些会议的主要目标之一是介绍开始研究人员在代表性理论的权力几何方法。这些会议的主题演讲将是2018年的Milen Yakimov和2019年的Lidia Angeleri Hugel。每个主讲人将给两个一小时的讲座，强调几何方法;这些会谈将是研究生和博士后研究人员访问。也将有其他既定的研究人员给出了几个临时讲座。讲座的其余部分将由其他参与者进行研究讲座。这些将包括与博士学位相关的研究生和博士后研究人员的讲座。论文会议将提供一个诱人的氛围，可以形成新的合作，年轻的研究人员将有机会了解表征理论中的尖端几何方法。此外，会议将使早期职业代表理论家介绍他们的工作，并与更广泛的研究社区互动。在过去的40年里，有限维代数的表示理论受到代数几何方法的极大影响，特别是几何不变理论和变换群。与此同时，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和表示论之间的这种相互作用。这些会议的主题将包括：量子幂零代数和量子簇代数; Poisson几何和簇的坐标环的量子化;倾斜和淤积理论;有界箭图的半不变量;簇代数的几何方面;模的退化和模簇中轨道闭包的几何;有限维代数的模问题;和泛变形环及其与模空间的联系。有关爱荷华州大学和密苏里-哥伦比亚大学几何方法表示理论会议的更多信息，请访问http://homepage.math.uiowa.edu/~fbleher/CGMRT.html.This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

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.