Symplectic Representation Theory

“辛表示理论”会议将于 2019 年 4 月 1 日至 5 日在法国马赛国际数学研究中心 (https://www.cirm-math.com) 举行。会议的主题是数学中一个快速发展的领域，它连接了数学和物理学等多个学科。会议的主要目标是了解重要的几何、物理和代数对象的结构，这些对象出现在很多地方，从而概括了半简单李代数以及李群和旗簇几何的研究。重要的例子包括代数对象，例如所谓的 Cherednik、Hecke 和箭袋代数；几何对象，例如超曲面和箭袋变体以及仿射格拉斯曼函数；以及物理对象，例如 3D 超对称量子场论的真空模空间。最近发生了许多重要的进展，使物理对象在数学上变得精确，解决了关于科祖尔对偶性、镜像对称和量子上同调的数学猜想，并找到了量子群和表示的几何构造以及李理论对象和新的概括。本次会议的目的是让参与者在这个快速发展的领域中走在知识的最前沿。选择主讲人是因为他们对最近的进展负有很大责任。这些演讲者的研究内容包括： 1) 库仑支的定义和基本性质、其量子化和三维镜像对称性； 2）我们对量子上同调及其对应的K理论的理解取得突破； 3）（几何）分类及其在组合表示理论中的应用； 4）规范理论、拓扑场论和膜范畴在辛表示论中的作用； 5）辛奇点的分类和结构、辛分辨率和量化。 会议网站的网址为 https://conferences.cirm-math.fr/1956.html。该奖项反映了 NSF 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 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.