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.

该奖项支持资助美国参与者参加将于 2019 年 1 月 7 日至 18 日在澳大利亚克莱斯威克墨尔本大学举行的“流形拓扑：高维和低维之间的相互作用”项目。 这次会议将汇集来自世界各地的学生、博士后和研究人员，以促进对多种理论中基本问题的研究。它将促进高维和低维拓扑研究人员之间的互动。 会议的结构如下：第一周由世界专家举办迷你课程，第二周举行会议。这两周的重点是开放问题和协作工作。这种结构将使早期职业研究人员受益匪浅。会议的另一个特点是该计划的主题：促进高维度和低维度的互动将减轻技术讨论和问题的趋势。本次会议主要有两个研究目的。 首先是从高维度和​​低维度之间的相互作用中确定协同作用的环境，并在这些环境中的问题上取得进展。第二是产生高质量的问题列表来指导流形拓扑的未来研究。预计会议期间的合作所产生的精心设计和公开的问题清单将为数学界带来长期利益。 n 流形是局部类似于 n 维欧几里得空间的空间。使用几何技术研究维度小于或等于 3 的流形。维数大于或等于 5 的流形通过外科手术理论进行研究，其中涉及代数和微分拓扑、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只取得了部分成功。该计划的需要是，这些领域在过去几十年中已经出现了分歧，以至于低/中/高维拓扑的研究人员通常并不总是了解其他维度的当前研究/技术。该计划预计将产生协同效应，使专家和新一代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- Between-topology-in-high-and-low-dimensions/ 上找到。该奖项反映了 NSF 的法定使命，并已通过使用基金会的智力优点和更广泛的影响审查标准进行评估，认为值得支持。