Conference on Homological Mirror Symmetry

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源镜像对称会议。镜像对称起源于物理学，是超共形量子场论之间的二象性。这种对偶性被解释为一个一致的，强大的数学框架，称为同质镜像对称（HMS），它导致了数学界如何从理论物理中获取思想的戏剧性发展，实际上是我们对空间本身的概念。今天，HMS被确立为最强大的框架之一，用于在现代几何中看似无关的部分之间建立桥梁。传统上，HMS在发现新现象和证明基于代数几何的辛拓扑和接触拓扑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，这些联系具有显著的代数应用，并为理性问题提供新的见解。会议将特别关注新的前沿研究方向：(1)双民族不变量和d模的胶合；(2)扩展了同调镜像对称的范围；(3)范畴Kaehler几何；(4)拓扑递归。该奖项反映了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，认为值得支持。

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.