Symplectic Representation Theory

University Of Texas At Austin, Austin TX

Investigators

Abstract

The conference "Symplectic Representation Theory" will take place at the Centre International de Rencontres Mathematiques (https://www.cirm-math.com), in Marseille, France, from April 1 to April 5, 2019. The subject of the conference is a rapidly developing field in mathematics which connects several disciplines, not only in mathematics but also in physics. The main goals of the conference are to understand the structure of important geometric, physical, and algebraic objects that appear in very many places that generalize the study of semi-simple Lie algebras and the geometry of Lie groups and flag varieties. Important examples included are algebraic objects such as the so-called Cherednik, Hecke, and quiver algebras; geometric objects such as hypertoric and quiver varieties and affine Grassmannians; and physical objects such as moduli spaces of vacua of 3D supersymmetric quantum field theories. Recently many important developments have occurred, making physical objects precise in mathematics, resolving mathematical conjectures about Koszul duality, mirror symmetry, and quantum cohomology, and finding geometric constructions of quantum groups and representations as well as Lie-theoretic objects and new generalizations. The aim of the proposed conference is to bring participants to the forefront of knowledge in this fast moving field. The keynote speakers are chosen because they are responsible for much of this recent progress. These speakers to give research talks about: 1) The definition, and fundamental properties, of the Coulomb branch, its quantizations, and three-dimensional mirror symmetry; 2) Breakthroughs in our understanding of quantum cohomology, and its K-theoretic counterpart; 3) (Geometric) categorification, and applications to combinatorial representation theory; 4) The role of gauge theory, topological field theories, and categories of branes in symplectic representation theory; and 5) The classification and structure of symplectic singularities, their symplectic resolutions, and quantizations. The conference website has the URL https://conferences.cirm-math.fr/1956.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.