Current Trends in Symplectic Topology

关于“辛拓扑的当前趋势”的暑期学校将于2019年7月1日至12日在蒙特利尔的CRM（数学研究中心）举行。辛拓扑是几何学中一个发展迅速的分支，在过去的二十年中有了惊人的发展。学校的目的是为不同群体的研究生和博士后研究人员提供接触这一学科的机会。该学院将由该领域领先研究人员的迷你课程、练习课程、年轻研究人员的精选演讲以及确定未来研究中心方向的开放式问题小组组成。该基金将为美国的研究生和博士后研究人员提供参加暑期学校的资金。这将通过提供重要前沿研究课题的培训来改善美国的劳动力。暑期学校将涵盖的主要主题是刚性与灵活性的二分法；深谷范畴与同调镜像对称；哈密顿动力学、容量和谱不变量；辛场论及其变体和应用；j全纯曲线模空间的基本性质。尽管最近有一些针对上述个别主题的专门会议，但暑期学校在将辛拓扑的这些不同方面综合为年轻研究人员可访问的概述方面是独一无二的。该奖项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知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

A summer school on "Current Trends in Symplectic Topology" will be held at the CRM (Centre de Recherches Mathematiques) in Montreal from July 1-12, 2019. Symplectic topology is a rapidly developing branch of geometry that has seen phenomenal growth in the last twenty years. The school is intended to provide access to this subject to a diverse group of graduate students and postdoctoral researchers. The school will consist of minicourses by leading researchers in the field, exercise sessions, selected talks by young researchers, and an open problems panel to identify central directions for future research. The grant will provide funding to enable US-based graduate students and postdoctoral researchers to participate in the summer school. This will improve the US workforce by providing training in important cutting-edge research topics.Major themes to be covered in the summer school are the dichotomy between rigidity and flexibility; the Fukaya category and homological mirror symmetry; Hamiltonian dynamics, capacities, and spectral invariants; symplectic field theory, its variants, and applications; and foundational properties of moduli spaces of J-holomorphic curves. Although there have been some recent specialized conferences on individual topics in the above list, the summer school is unique in synthesizing these different aspects of symplectic topology into an overview accessible to young researchers.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.