Topology of Manifolds: Interactions between High and Low Dimensions

流形拓扑：高维和低维之间的相互作用

• 批准号: 1850620
• 负责人: James Davis
• 金额: $ 3万
• 依托单位: Indiana University
• 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: 2019-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1850620&HistoricalAwards=false
• 关键词: Topology; Manifolds; Interactions; between; Low

This award supports funding for the participation of US-based participants in the program "Topology of Manifolds: interactions between high and low dimensions" to be held January 7-18, 2019 at the University of Melbourne, Creswick, Australia. This meeting will bring together students, postdocs, and researchers from all over the world to stimulate research on fundamental questions in manifold theory. It will promote the interaction between researchers in high and low dimensional topology. The meeting is structured as follows: mini-courses in the first week by world experts and a conference in the second week. Both weeks focus on open problems and collaborative work. This structure will greatly benefit early career researchers. Another feature of the meeting that will make it accessible is the theme of the program: promoting interactions high and low dimensions will mitigate the tendency of technical talks and problems. There are two main research aims for this meeting. The first is to identify settings for synergy from the interaction between high and low dimensions and to make progress on problems in these settings. The second is to produce a high-quality problem list to guide future research in manifold topology. It is expected that a well-crafted and publicized problem list arising from the collaboration during the meeting will be of long-term benefit to the mathematical community.An n-manifold is a space which locally resembles n-dimensional Euclidean space. Manifolds of dimension less or equal than 3 are studied using geometric techniques. Manifolds of dimension greater or equal than 5 are studied via surgery theory, which involves a mix of algebraic and differential topology, algebra, and analysis. Dimension 4 is in between; both the high dimensional Whitney Trick and the low-dimensional geometric techniques are only partially successful. The need for the program is that these areas have diverged in the last several decades, to the extent that, often researchers in low/middle/high dimensional topology are not always aware of the current research/techniques in other dimensions. This program is expected to lead to a synergy, benefiting both the experts and the new generation of early career researchers. The website for the event can be found at https://www.matrix-inst.org.au/events/interactions-between-topology-in-high-and-low-dimensions/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.

该奖项支持基于美国参与者参加“流形拓扑：高维拓扑：高维和低维度之间的互动”计划的资金，将于2019年1月7日至18日在澳大利亚克雷斯威克墨尔本大学举行。 这次会议将召集来自世界各地的学生，博士后和研究人员，以刺激对多种理论中基本问题的研究。它将促进高维拓扑和低维拓扑的研究人员之间的相互作用。 会议的结构如下：世界专家在第一周在第一周和第二周举行的会议。这两个星期都关注开放问题和协作工作。这种结构将极大地使早期的职业研究人员受益。会议的另一个功能将使之可访问该计划的主题：促进高维度和低维度的互动将减轻技术谈话和问题的趋势。这次会议有两个主要的研究目的。 首先是通过高维和低维之间的相互作用来确定协同作用的设置，并在这些设置中的问题上取得进展。第二个是产生高质量的问题清单，以指导多种拓扑中的未来研究。可以预期，会议期间的合作产生的精心制作且公开的问题清单将对数学社区带来长期利益。一个N-Manifold是一个本地类似于N维欧几里得空间的空间。使用几何技术研究尺寸的歧管小于或等于3。维度的歧管通过手术理论研究了大于或等于5的歧管，该理论涉及代数和差异拓扑，代数和分析的混合。维度4介于两者之间；高维惠特尼技巧和低维几何技术都仅在部分成功。该计划的需求是，在过去的几十年中，这些领域在某种程度上已经有所不同，以至于通常，低/中/高维拓扑的研究人员并不总是意识到其他维度中当前的研究/技术。预计该计划将导致协同作用，从而使专家和新一代的早期职业研究人员受益。该活动的网站可以在https://www.matrix-inst.org.au/events/interactions/interactions-between-topology-in-topology-in-high-ang-and-low-dimensions/this Award中反映出NSF的法定任务，并通过该基金会的知识分子优点和广泛的影响来评估NSF的法定任务。