Symplectic Representation Theory

“辛表示理论”会议将于2019年4月1日至4月5日在法国马赛的国际Rencontres数学中心（https://www.cirm-math.com）举行。这次会议的主题是一个迅速发展的数学领域，它不仅涉及数学，而且涉及物理等多个学科。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，这些对象出现在许多地方，推广了半简单李代数和李群和旗变的几何研究。重要的例子包括代数对象，如所谓的Cherednik， Hecke和quiver代数；几何对象，如高曲型和颤抖型以及仿射格拉斯曼型；以及三维超对称量子场论中的真空模空间等物理对象。最近发生了许多重要的发展，使物理对象在数学上精确，解决了关于科祖尔对偶、镜像对称和量子上同调的数学猜想，发现了量子群和表示的几何结构，以及李论对象和新的推广。本次会议的目的是将与会者带到这一快速发展领域的前沿知识。选择主讲人是因为他们对最近的进展负有很大的责任。这些讲者的研究内容包括：1)库仑分支的定义、基本性质、量子化和三维镜像对称性；2)对量子上同调及其k理论对应物的理解取得突破；（几何）分类及其在组合表示理论中的应用；4)规范论、拓扑场论和膜的范畴在辛表示理论中的作用；5)辛奇异点的分类、结构、辛分解和量子化。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知识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.