Topology of Manifolds: Interactions between High and Low Dimensions

该奖项支持资助美国参与者参加将于2019年1月7日至18日在澳大利亚克雷斯威克墨尔本大学举行的“流形拓扑：高维度和低维度之间的相互作用”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，以促进对流形理论中基本问题的研究。它将促进高、低维拓扑学研究者之间的交流。 会议安排如下：第一周由世界专家举办小型课程，第二周举行会议。这两个星期都集中在开放的问题和协作工作。这种结构将大大有利于早期的职业研究人员。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会谈和问题的倾向。这次会议有两个主要的研究目标。 第一个是从高维度和低维度之间的相互作用中确定协同作用的设置，并在这些设置中的问题上取得进展。第二个是产生一个高质量的问题列表，以指导未来的研究在流形拓扑。预计在会议期间合作产生的精心制作和公布的问题清单将对数学界产生长远的利益。n-流形是局部类似于n维欧氏空间的空间。流形的维数小于或等于3的研究使用几何技术。流形的尺寸大于或等于5研究通过手术理论，其中涉及代数和微分拓扑，代数和分析的混合。4维介于两者之间;高维惠特尼技巧和低维几何技术都只是部分成功。该计划的必要性在于，这些领域在过去几十年中出现了分歧，以至于低/中/高维拓扑学的研究人员往往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作用，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www.example.com上找到https://www.matrix-inst.org.au/events/interactions-between-topology-in-high-and-low-dimensions/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。

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.