Conference: 1, 2, 3: Curves, Surfaces, and 3-Manifolds

会议：1,2,3：曲线、曲面和 3-流形

• 批准号: 2246832
• 负责人: Christopher Leininger
• 金额: $ 2.8万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-05-01 至 2025-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2246832&HistoricalAwards=false
• 关键词: Conference; Curves; Surfaces; Manifolds

This NSF award provides partial support for U.S. based participants of a conference titled "1, 2, 3; Curves, Surfaces, and 3-Manifolds" in Nahsholim Israel and the Technion Institute of Technology, May 7-11, 2023. The goal of the conference is to bring together researchers at all career stages to discuss intersections in geometry and topology in dimensions 1, 2, and 3. These topics have become intimately intertwined over the past 40 years, and have provided the impetus for the much of the development of entire fields of mathematics, such as geometric group theory. Importantly, the conference will also include workshop-style talks aimed at helping bridge the gap between seasoned researchers and the next generation of mathematicians.The confluence of topology and geometry of three dimensional manifolds, and the geometric properties of mapping class groups, has been intensively studied over the last several decades and is of central importance in a variety of mathematical disciplines. For example, hyperbolic 3-manifolds are often governed by certain surfaces contained in them. These surfaces inherit their own hyperbolic structures from their inclusion into the 3-manifold, and these structures are very coarsely encoded by collections of curves on the surface. Miraculously, in key situations, the hyperbolic 3-manifold can be reconstituted from this collection of curves--this is the essential content of the Ending Lamination Theorem. The mathematics developed to study curves used in the proof of this theorem simultaneously provide a powerful toolkit for studying mapping class groups of surfaces. Abstractions of these tools now provide the framework for studying a very large and robust class of groups from a geometric perspective. More details can be found on the conference website: https://cms-math.net.technion.ac.il/123-curves-surfaces-and-3-manifolds/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 NSF 奖项为 2023 年 5 月 7 日至 11 日在以色列 Nahsholim 和以色列理工学院举行的题为“1,2,3；曲线、曲面和 3-流形”的会议的美国参与者提供部分支持。这次会议将汇集各个职业阶段的研究人员，讨论 1、2 和 3 维几何和拓扑的交叉点。这些主题已经紧密地交织在一起过去 40 年来，为整个数学领域（例如几何群论）的发展提供了很大的推动力。 重要的是，会议还将包括研讨会式的演讲，旨在帮助缩小经验丰富的研究人员和下一代数学家之间的差距。三维流形的拓扑和几何的融合，以及映射类群的几何性质，已经得到了深入的研究。在过去的几十年里进行了研究，并且在各种数学学科中都具有核心重要性。 例如，双曲 3 流形通常受其中包含的某些表面控制。 这些曲面从包含到 3 流形中继承了它们自己的双曲结构，并且这些结构由曲面上的曲线集合非常粗略地编码。 神奇的是，在关键情况下，双曲3流形可以从这组曲线中重构出来——这就是终结叠层定理的本质内容。 为研究该定理证明中使用的曲线而开发的数学同时为研究曲面的映射类组提供了强大的工具包。 这些工具的抽象现在提供了从几何角度研究非常大且强大的群类的框架。 更多详细信息可以在会议网站上找到：https://cms-math.net.technion.ac.il/123-curves-surfaces-and-3-manifolds/该奖项反映了 NSF 的法定使命，并被认为值得通过使用基金会的智力优势和更广泛的影响审查标准进行评估来提供支持。