Conference on Homological Mirror Symmetry

同调镜像对称会议

• 批准号: 2001614
• 负责人: Ludmil Katzarkov
• 金额: $ 2万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-02-01 至 2023-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2001614&HistoricalAwards=false
• 关键词: Conference; Homological; Mirror; Symmetry

This award supports participation in a conference on Homological Mirror Symmetry to be held at the University of Miami from January 27 through February 31, 2020. Mirror symmetry originated in physics as a duality between superconformal quantum field theories. This duality has been interpreted in a consistent, powerful mathematical framework called Homological Mirror Symmetry (HMS) that has led to dramatic developments in how the mathematical community approaches ideas from theoretical physics, and indeed our conception of space itself. Today HMS is established as one of the most powerful frameworks for building bridges between seemingly unrelated parts of modern geometry. Traditionally HMS has been incredibly successful in discovering novel phenomena and proving unexpected results in symplectic and contact topology informed by algebraic geometry. The goal of this conference is to highlight the flow of ideas in the opposite direction: from symplectic to complex geometry. The conference will summarize recently developed connections between Hodge Theory and HMS which have striking algebraic applications and give new insights into rationality problems. In particular, the conference will focus on new cutting-edge directions of investigation: (1) birational invariants and gluing of D-modules; (2) extending the scope of Homological Mirror Symmetry; (3) categorical Kaehler geometry; and (4) topological recursion. The conference website is https://schms.math.berkeley.edu/events/miami2020/.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.

该奖项支持参加将于1月27日至2020年2月31日在迈阿密大学举行的同源镜子对称会议。镜面的对称性起源于物理学，是超规格量子场理论之间的双重性。这种二元性是用一个一致，强大的数学框架来解释的，称为同源镜对称性（HMS），这导致了数学社区如何从理论物理学以及我们对空间本身的概念中探索思想的方式。如今，HMS已被确定为在现代几何形状看似无关的部分之间建造桥梁的最强大框架之一。 传统上，HMS在发现新现象并以代数几何形状告知的符号和接触拓扑结构的意外结果方面取得了令人难以置信的成功。这次会议的目的是朝着相反的方向强调思想的流动：从符号到复杂的几何形状。该会议将总结霍奇理论与HMS的最近建立的联系，这些联系具有引人注目的代数应用，并给出了对理性问题的新见解。特别是，该会议将重点介绍新的调查的新尖端方向：（1）D-Modules的生育不变性和粘合； （2）扩展同源镜对称的范围； （3）分类Kaehler几何形状； （4）拓扑递归。会议网站是https://schms.math.berkeley.edu/events/miami2020/.this奖，反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响来通过评估来支持的。