Graduate student workshop in symplectic and contact geometry

辛几何和接触几何研究生研讨会

• 批准号: 1722470
• 负责人: Eleny-Nicoleta Ionel
• 金额: $ 2.77万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-04-01 至 2019-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1722470&HistoricalAwards=false
• 关键词: Graduate; student; workshop; symplectic; contact

This National Science Foundation award provides partial support for a workshop to be held May 19-25, 2017 at Truckee, California. This workshop aims to introduce aspiring mathematicians in the fields of symplectic and contact geometry and from many institutions to vibrant areas of research, fostering collaboration, forming strong research ties between young researchers, and thus promoting future collaboration and research. The workshop is specifically designed to encourage the development of a diverse group of researchers in the fields of symplectic and contact geometry. It is a week-long intensive workshop, in which all activities occur under one roof. The lectures are delivered by the graduate student participants with the help of three mentors: Roger Casals (MIT), Laura Starkston (Stanford), and Steven Sivek (Bonn), who are emerging expert researchers in the field. This setup enhances communication skills, encourages active involvement or the participants and forging new collaborations.The topic of the 2017 workshop is symplectic fillings of contact manifolds, a topic with both a rich history and lots of new ideas that are currently being developed. One major aspect of the modern understanding of symplectic fillings is via an ever-growing dichotomy in symplectic and contact geometry: flexibility versus rigidity. Some fillings can be flexible, in which case they are completely determined up to isomorphism by differential-topological data; otherwise, there is a hope that some count of J-holomorphic curves implies that the symplectic geometry is more nuanced than the underlying differential topology. One goal of the workshop is to form bridges between these two different perspectives. Notes from the lectures and further information will be available on the website https://kylerec.wordpress.com/

这项国家科学基金会奖为将于2017年5月19日至25日在加利福尼亚州Truckee举行的研讨会提供部分支持。这次研讨会的目的是将辛几何和接触几何领域的有抱负的数学家以及来自许多机构的有抱负的数学家介绍到充满活力的研究领域，促进合作，在年轻研究人员之间建立牢固的研究联系，从而促进未来的合作和研究。该研讨会是专门为鼓励在辛几何和接触几何领域的不同研究人员的发展而设计的。这是一个为期一周的密集研讨会，所有活动都在一个屋檐下进行。讲座由研究生学员在三位导师的帮助下进行：罗杰·卡萨尔斯(麻省理工学院)、劳拉·斯塔克斯顿(斯坦福)和史蒂文·西韦克(波恩)，他们都是该领域的新兴专家研究人员。这种设置增强了沟通技能，鼓励参与者积极参与并打造新的合作。2017年研讨会的主题是接触流形的辛填充，这是一个既有丰富历史又有许多目前正在开发的新想法的主题。现代对辛填充的理解的一个主要方面是通过辛几何和接触几何中不断增长的二分法：柔韧性和刚性。一些填充可以是灵活的，在这种情况下，它们完全由微分拓扑数据同构来确定；否则，人们希望J-全纯曲线的一些计数意味着辛几何比基本的微分拓扑更细微。研讨会的目标之一是在这两种不同的视角之间架起桥梁。讲座笔记和更多信息可在网站https://kylerec.wordpress.com/上查阅