Topology in Dimensions 3, 3.5 and 4

3、3.5 和 4 维拓扑

• 批准号: 1818493
• 负责人: Ian Agol
• 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: 2018
• 资助国家: 美国
• 起止时间: 2018-06-01 至 2019-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818493&HistoricalAwards=false
• 关键词: Topology; Dimensions; 3.5

This National Science Foundation award provides partial support for the Conference on Topology in Dimensions 3, 3.5 and 4, to be held at the University of California Berkeley from June 25 to 29, 2018. Topology studies the mathematical properties of "spaces," from the physical 3-dimensional space and 4-dimensional space-time in which we carry out our daily lives, to much more abstract spaces such as the space of all possible configurations of a robot or all possible solutions to an equation. This conference will bring together researchers working on the interplay between three and four dimensional topology to share state of the art knowledge, hear talks from a select group of internationally renowned experts, and develop new collaborations. This grant will support travel expenses for graduate students, early career researchers and speakers.There is a fundamental nexus of problems, including the smooth 4-dimensional Schonflies and Poincare conjectures and their connection to decompositions of 3-manifolds, which is deeply rooted in and has long motivated the work of Abby Thompson (working mostly in dimension 3), Marty Scharlemann (working in 3.5-dimensional topology), and Rob Kirby (working mostly in dimension 4). This conference uses the collective legacy of these researchers as an organizing theme with the goal of reinvigorating work on these foundational problems, reminding the community of the power of their tools, and showcasing recent topological advances in the spirit of their work. Speakers will share old and new ideas and participants will have sufficient time for discussion with each other and with the speakers and for the forging of new collaborations. We have specifically asked certain speakers to give historical talks to help maintain continuity with the past as our rapidly developing field moves into the future. These talks will be of especial benefit to students and younger researchers, and will also help in the process of archiving the mathematical past. The conference website is at https://sites.google.com/sjsu.edu/thompscharbyfest/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.

这个国家科学基金会奖提供部分支持拓扑会议在尺寸3，3.5和4，将于6月25日至29日在加州伯克利大学举行，2018年。拓扑学研究“空间”的数学性质，从我们日常生活中的物理三维空间和四维时空，到更抽象的空间，如机器人的所有可能配置或方程的所有可能解的空间。本次会议将汇集研究三维和四维拓扑结构之间相互作用的研究人员，分享最先进的知识，听取国际知名专家的演讲，并发展新的合作。这项拨款将支持研究生，早期职业研究人员和演讲者的差旅费。有一个基本的问题，包括光滑的四维Schonflies和庞加莱拓扑及其与三维流形分解的联系，这深深植根于Abby Thompson的工作，并长期激励着他的工作（主要研究3维）、Marty Scharlemann（研究3.5维拓扑）和Rob Kirby（主要研究4维）。本次会议使用这些研究人员的集体遗产作为组织主题，目标是重振这些基础问题的工作，提醒社区他们的工具的力量，并展示他们工作精神的最新拓扑学进展。发言者将分享新旧思想，与会者将有足够的时间相互讨论，并与发言者讨论，并建立新的合作关系。我们特别要求某些演讲者进行历史性的演讲，以帮助我们在快速发展的领域走向未来时保持与过去的连续性。这些会谈将特别有利于学生和年轻的研究人员，也将有助于在存档的过程中的数学过去。会议网站是https://sites.google.com/sjsu.edu/thompscharbyfest/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。