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

该奖项为美国数学家参加将于2019年6月17日至21日在法国卢明国际数学中心（CIRM）举行的几何群论国际会议提供部分支持。这次会议将汇集来自美国、欧洲和亚洲的大约120名数学家。除了22场全体讲座外，还将有一场闪电会谈，早期的职业数学家将有机会展示他们的工作。该奖项将支持大约30名美国数学家出席会议。几何群论是20世纪80年代Gromov的工作中出现的一个相对较新的数学分支，它将群作为几何对象的经典处理置于更广泛的背景下。这个领域现在相当大，并且与许多不同的数学领域相互作用，包括低维拓扑、流形拓扑、复杂动力学、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，然后利用空间的性质来推断群的性质。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Gromov的另一个核心见解是黎曼几何中负曲率空间的许多性质具有“粗糙”的类似物，这是研究群几何的自然环境。对作用于具有粗糙版本的非正曲率和负曲率的空间的群的研究将是这个为期一周的会议的焦点。有关会议的更多信息可在https://conferences.cirm-math.fr/1958.html.This上找到。奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.