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

第六届和第七届表征理论几何方法会议将于2018年11月17日至19日在爱荷华大学举行，2019年11月23日至25日在密苏里大学举行。表示论是研究线性空间对称性的现代代数的一个分支。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。几何方法在这些领域变得越来越重要。这些会议的主要目的之一是向表示理论的初学者介绍几何方法的力量。2018年Milen Yakimov和2019年Lidia Angeleri Hugel将分别为这些会议的主题演讲。每位主讲人将进行两次一小时的讲座，重点介绍几何方法；这些讲座将对研究生和博士后研究人员开放。也会有一些由其他知名研究人员提供的说明性讲座。其余的讲座将由其他参与者进行研究报告。这些讲座将包括研究生和博士后研究人员与他们的博士论文相关的讲座。会议将提供一个吸引人的氛围，可以形成新的合作，年轻的研究人员将有机会学习表征理论中的前沿几何方法。此外，会议将使早期职业的表征理论家能够展示他们的工作，并与更广泛的研究团体进行互动。近40年来，有限维代数的表示理论受到了代数几何方法，特别是几何不变量理论和变换群方法的巨大影响。同时，这种影响导致了从表征理论到几何的思想和技术的反馈。表征理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征理论之间的相互作用。这些会议的主题将包括：量子幂零代数和量子簇代数；变量坐标环的泊松几何及其量化倾斜和淤积理论；约束颤振的半不变量；簇代数的几何方面；模的退化和模的轨道闭包几何有限维代数的模问题通用变形环及其与模空间的联系。关于爱荷华大学和密苏里-哥伦比亚大学的几何方法表征理论会议的更多信息可以在http://homepage.math.uiowa.edu/~fbleher/CGMRT.html.This上找到，该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.