Conference on Artin Groups, CAT(0) Geometry, and Related Topics

该奖项为美国数学家参加将于2020年6月1日至5日在法国卢米尼举行的CIRM（国际数学会议中心）举行的国际会议“Artin群，CAT（0）几何及相关主题”提供部分支持。本次几何群论国际会议预计约有80-85人参加。组织者将做出特别努力，包括研究生和博士后的多元化群体，该计划将纳入鼓励他们与更多知名数学家互动的机制。会议的主题可以广泛地描述为使用几何方法来研究代数对象。更具体地说，这个想法是通过将群实现为某个空间的对称群来研究群，然后使用空间的几何特征（如曲率）来得出关于群的结论。这门学科被称为几何群论，近年来得到了极大的发展，现在已经成为数学界的一个主流。本次会议将突出几何群论中两个主要主题之间的相互作用：一方面是Artin群，另一方面是CAT（0）几何。也许阿廷群最著名的例子是辫子群。Artin群的研究涉及许多不同的领域，包括低维拓扑、奇点理论、代数拓扑和数学物理。CAT（0）空间被引入作为非正弯曲流形的合成模拟。CAT（0）空间的对称群具有很强的代数性质，使其成为几何群论的理想工具。虽然Artin群和CAT（0）几何及其密切关系将是会议的统一主题，但相关主题，如Coxeter群，三维流形，自由群的自同构和映射类群也将包括在内，以丰富与会者之间的交流并激发新研究项目的想法。会议的详细信息和注册信息可以在www.example.com上找到https://conferences.cirm-math.fr/2159.html.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 provides partial support for participation by US-based mathematicians at the international conference "Artin Groups, CAT(0) Geometry, and Related Topics" to be held at the CIRM (Centre International de Rencontres Mathematiques) in Luminy, France from June 1-5 of 2020. This international meeting on geometric group theory is expected to have about 80-85 participants. The organizers will make a special effort to include a diverse group of graduate students and postdocs, and the program will incorporate mechanisms for encouraging their interaction with more established mathematicians. The subject of the conference can be broadly described as using geometric methods to study algebraic objects. More specifically, the idea is to study groups by realizing them as groups of symmetries of some space, then to use geometric features of the space such as curvature to draw conclusions about the group. This subject, called geometric group theory, has expanded dramatically in recent years and is now a major current in mathematics. This conference will highlight the interaction between two main themes in geometric group theory: Artin groups on the one hand, and CAT(0) geometry on the other. Perhaps the most well-known examples of Artin groups are the braid groups. The study of Artin groups touches on many different fields, including low-dimensional topology, singularity theory, algebraic topology, and mathematical physics. CAT(0) spaces were introduced as a synthetic analog of non-positively curved manifolds. The symmetry groups of CAT(0) spaces turn out to have strong algebraic properties, making them an ideal tool for geometric group theory. Although Artin groups and CAT(0) geometry and their strong relationship will be the unifying theme of the conference, related topics such as Coxeter groups, three-dimensional manifolds, automorphisms of free groups, and mapping class groups will also be included in order to enrich exchanges between participants and inspire ideas for new research projects. Details of the conference and registration information may be found at https://conferences.cirm-math.fr/2159.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.