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。这种二重性已经在一个一致的、强大的数学框架中得到了解释，这个框架被称为同调镜像对称（HMS），它导致了数学界如何从理论物理学中获得思想的戏剧性发展，实际上也是我们对空间本身的概念。今天，HMS被确立为在现代几何看似无关的部分之间建立桥梁的最强大的框架之一。 传统上，HMS在发现新现象和证明由代数几何告知的辛和接触拓扑中的意想不到的结果方面取得了令人难以置信的成功。本次会议的目标是突出思想的流动在相反的方向：从辛复杂的几何。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，并对合理性问题提出新的见解。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-模的粘合;（2）扩展同调镜像对称的范围;（3）分类Kaehler几何;和（4）拓扑递归。会议网站是https://schms.math.berkeley.edu/events/miami2020/.This奖反映了NSF的法定使命，并已被认为值得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的支持。

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.