Student workshop in symplectic and contact geometry

辛几何和接触几何学生研讨会

• 批准号: 2002676
• 负责人: Eleny-Nicoleta Ionel
• 金额: $ 9.53万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-04-01 至 2026-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2002676&HistoricalAwards=false
• 关键词: Student; workshop; symplectic; contact; geometry

This award provides support for the next three editions of the Kylerec Student Workshop (2020, 2021 and 2022), starting with its 2020 edition to be held from July 20 to July 24 in Big Bear Lake, CA. The Kylerec 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 to four mentors, who are emerging expert researchers in the field. This setup enhances communication skills, encourages active involvement of the participants and forging new collaborations.The student organizers for the 2020 Kylerec workshop are Orsola Capovilla-Searle (Duke University), Dahye Cho (Stony Brook University), Francois-Simon Fauteux-Chapleau (Stanford University), Tim Large (MIT) and Sarah McConnell (Stanford University). The topic is Quantitative Symplectic Geometry, with a focus on symplectic embedding problems. The deceptively simple question of when does one symplectic manifold embed inside another, and the subtle dependance of this question on quantitative parameters, has been a focal point of the subject for the last thirty years. Since Gromov's celebrated non-squeezing result, a variety of techniques drawing upon ideas in dynamical systems, toric algebraic geometry and four-dimensional gauge theory have been used to better understand such problems; yet a systematic understanding has eluded researchers thus far. The objective of the 2020 Kylerec workshop is to understand the current state of knowledge on such questions, covering both the methods researchers have developed to produce surprising symplectic embeddings, as well as the technical tools of Floer theory and embedded contact homology that have been used to provide state-of-the-art obstructions to the existence of a symplectic embedding. The web site for the Kylerec workshops is https://kylerec.wordpress.com/.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.

该奖项为接下来三届Kylerec学生研讨会（2020年、2021年和2022年）提供支持，从7月20日至7月24日在加利福尼亚州大熊湖举行的2020年研讨会开始。 Kylerec研讨会旨在介绍辛几何和接触几何领域的有抱负的数学家，并从许多机构到充满活力的研究领域，促进合作，在年轻研究人员之间形成强大的研究联系，从而促进未来的合作和研究。该研讨会是专门设计的，以鼓励在辛和接触几何领域的研究人员的多样化的发展。这是一个为期一周的密集讲习班，所有活动都在同一个屋檐下进行。讲座由研究生参与者在三到四名导师的帮助下进行，他们是该领域的新兴专家研究人员。2020年Kylerec研讨会的学生组织者是Orsola Capovilla-Searle（杜克大学），Dahye Cho（斯托尼布鲁克大学），Francois-Simon Fauteux-Chapleau（斯坦福大学），Tim Large（麻省理工学院）和Sarah McConnell（斯坦福大学）。题目是定量辛几何，重点是辛嵌入问题。一个辛流形何时嵌入另一个辛流形，这个看似简单的问题，以及这个问题对定量参数的微妙依赖，在过去的30年里一直是这个主题的焦点。自从格罗莫夫的非压缩结果之后，各种利用动力系统、复曲面代数几何和四维规范理论的技术被用来更好地理解这些问题;然而，迄今为止，研究人员还没有系统的理解。2020年Kylerec研讨会的目的是了解这些问题的知识现状，包括研究人员开发的产生令人惊讶的辛嵌入的方法，以及Floer理论和嵌入式接触同源的技术工具，这些技术工具已被用于提供最先进的障碍辛嵌入的存在。Kylerec研讨会的网站是https://kylerec.wordpress.com/.This奖项反映了NSF的法定使命，并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来支持。