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

University Of Iowa, Iowa City IA

Investigators

Abstract

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.