Current Trends in Symplectic Topology

辛拓扑的当前趋势

• 批准号: 1916934
• 负责人: Michael Hutchings
• 金额: $ 1.5万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916934&HistoricalAwards=false
• 关键词: Current; Trends; Symplectic; Topology

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.

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。辛拓扑学是几何学的一个迅速发展的分支，在过去的二十年里有了惊人的发展。学校旨在为研究生和博士后研究人员提供这一主题的机会。该学校将由该领域领先研究人员的小型课程，练习课程，年轻研究人员的精选讲座以及一个开放式问题小组组成，以确定未来研究的中心方向。这笔赠款将提供资金，使美国的研究生和博士后研究人员能够参加暑期学校。这将通过提供重要的前沿研究课题的培训来提高美国的劳动力。暑期学校的主要主题包括刚性和柔性之间的二分法;福谷范畴和同调镜像对称;哈密顿动力学、容量和谱不变量;辛场论、其变体和应用;以及J-全纯曲线模空间的基本性质。虽然最近有一些关于上述主题的专门会议，但暑期学校在将辛拓扑的这些不同方面综合成年轻研究人员可以访问的概述方面是独一无二的。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，被认为值得支持。