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.

“辛表示理论”会议将于2019年4月1日至4月5日在法国马赛国际伦孔特数学中心(https://www.cirm-math.com)，)举行。会议的主题是一个迅速发展的数学领域，它连接了几个学科，不仅在数学上，而且在物理上。会议的主要目标是了解在许多地方出现的重要几何、物理和代数对象的结构，这些对象推广了对半单李代数以及李群和旗簇的几何的研究。重要的例子包括代数对象，如所谓的Cherednik、Hecke和箭图代数；几何对象，如超环变簇、箭图簇和仿射Grassmannians；以及物理对象，如三维超对称量子场论的真空模空间。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Koszul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。会议的目的是将与会者带到这个快速发展的领域的知识的前沿。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。这些发言者的研究内容包括：1)库仑分支、它的量子化和三维镜像对称性的定义和基本性质；2)我们对量子上同调及其K理论的理解的突破；3)(几何)分类，以及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理论中的作用；5)辛奇点的分类和结构、辛解和量子化。会议网站上的URL https://conferences.cirm-math.fr/1956.html.This奖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智力优势和更广泛的影响审查标准进行评估，被认为值得支持。