Conference on Aspects of Non-Positive and Negative Curvature in Group Theory

群论中非正曲率和负曲率方面的会议

• 批准号: 1856388
• 负责人: Kenneth Bromberg
• 金额: $ 3万
• 依托单位: University of Utah
• 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: 2019-06-01 至 2023-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1856388&HistoricalAwards=false
• 关键词: Conference; Aspects; Non; Positive; Negative

This award provides partial support for participation by US-based mathematicians at an international conference on geometric group theory to be held at the CIRM (Centre International de Rencontres Mathematiques) in Luminy, France from June 17-21 of 2019. The conference will bring together a diverse group of approximately 120 mathematicians from the US, Europe and Asia. Along with twenty-two plenary lectures there will be a session of lightning talks where early career mathematicians will have the chance to present their work. This award will support the attendance of approximately 30 US-based mathematicians at the conference. Geometric group theory is a relatively recently recognized subfield of mathematics emerging from Gromov's work in the 1980s, which put the classical treatment of groups as geometric objects in a far broader context. The field is now quite large, and has interactions with many different fields of mathematics including low-dimensional topology, the topology of manifolds, complex dynamics, combinatorial group theory, logic and the study of various classical families of groups. The central idea of geometric group theory is to study a group through an action (typically an isometric one) on some space (typically a metric space) and then use properties of the space to deduce properties of the group. Perhaps the most successful instance of this is when the space has some form of negative curvature. While classically curvature is a concept of Riemannian geometry, another central insight of Gromov is that many properties of spaces of negative curvature in Riemannian geometry have "coarse" analogues and that this is the natural setting to study the geometry of groups. The study of groups that act on spaces with coarse versions of non-positive and negative curvature will be the focus of this week long conference. More information on the conference can be found at https://conferences.cirm-math.fr/1958.html.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.

该奖项为美国数学家参加将于 2019 年 6 月 17 日至 21 日在法国卢米尼 CIRM（国际数学研究中心）举行的几何群理论国际会议提供部分支持。该会议将汇集由来自美国、欧洲和亚洲的大约 120 名数学家组成的多元化团体。除了 22 场全体演讲之外，还将举办一场闪电演讲，早期职业数学家将有机会展示他们的工作。该奖项将支持约 30 名美国数学家参加此次会议。几何群论是一个相对较新被认可的数学子领域，它诞生于格罗莫夫在 20 世纪 80 年代的工作中，它将群作为几何对象的经典处理置于更广泛的背景下。该领域现在相当大，并且与许多不同的数学领域有相互作用，包括低维拓扑、流形拓扑、复动力学、组合群论、逻辑和各种经典群族的研究。几何群论的中心思想是通过在某个空间（通常是度量空间）上的作用（通常是等距作用）来研究群，然后利用该空间的性质来推导群的性质。也许最成功的例子是当空间具有某种形式的负曲率时。虽然经典曲率是黎曼几何的一个概念，但格罗莫夫的另一个中心见解是，黎曼几何中负曲率空间的许多性质都有“粗略”的类似物，这是研究群几何的自然背景。对作用于具有粗略版本的非正曲率和负曲率空间的群的研究将是本周会议的焦点。有关会议的更多信息，请访问 https://conferences.cirm-math.fr/1958.html。该奖项反映了 NSF 的法定使命，并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，被认为值得支持。