Symplectic Representation Theory

辛表示论

• 批准号: 1906141
• 负责人: David Ben-Zvi
• 金额: $ 3万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-02-15 至 2020-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1906141&HistoricalAwards=false
• 关键词: Symplectic; Representation; Theory

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.

会议“辛表示理论”将于2019年4月1日至4月5日在法国马赛的国际数学会议中心（https：//www.example.com）举行。www.cirm-math.com会议的主题是一个快速发展的数学领域，它连接了几个学科，不仅在数学，而且在物理学。会议的主要目标是了解出现在许多地方的重要几何，物理和代数对象的结构，这些对象概括了半单李代数和李群几何的研究。重要的例子包括代数对象，如所谓的Cherednik，Hecke和Cherednik代数;几何对象，如hypertoric和hypertoric品种和仿射Grassmannian;和物理对象，如模空间的真空的3D超对称量子场论。最近发生了许多重要的发展，使物理对象精确的数学，解决数学命题约Koszul对偶，镜像对称，和量子上同调，并发现几何结构的量子群和表示，以及李群理论的对象和新的generalizations.The目的提出会议是把与会者的知识前沿在这个快速发展的领域。之所以选择主旨发言人，是因为他们对最近的进展负有很大责任。这些演讲者将提供以下研究讲座：1）库仑分支的定义和基本性质，它的量子化和三维镜像对称; 2）我们对量子上同调的理解的突破，以及它的K理论对应物; 3）（几何）分类及其在组合表示论中的应用; 4）规范论、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，它们的辛分解和量子化。 会议网站的URL为https://conferences.cirm-math.fr/1956.html.This奖项反映了NSF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。