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 2020 年 1 月 27 日至 2 月 31 日在迈阿密大学举行的同调镜像对称会议。镜像对称起源于物理学，是超共形量子场论之间的对偶性。这种二元性已在称为同调镜像对称（HMS）的一致、强大的数学框架中得到解释，该框架导致数学界在处理理论物理学思想以及我们对空间本身的概念方面取得了巨大的发展。如今，HMS 已成为最强大的框架之一，用于在现代几何看似不相关的部分之间架起桥梁。 传统上，HMS 在发现新现象并证明代数几何所揭示的辛和接触拓扑中的意外结果方面取得了令人难以置信的成功。这次会议的目标是强调相反方向的思想流动：从辛几何到复杂几何。会议将总结霍奇理论和 HMS 之间最近发展的联系，这些联系具有惊人的代数应用，并为理性问题提供了新的见解。特别是，会议将重点关注新的前沿研究方向：（1）双有理不变量和D-模粘合； (2)扩展同调镜像对称的范围； (3) 分类凯勒几何； (4)拓扑递归。会议网站为 https://schms.math.berkeley.edu/events/miami2020/。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，认为值得支持。