Geometry, Arithmetic, and Groups.

由来自美国各地的研究人员组织的关于几何、算术和小组的会议将于2022年6月20日至24日在德克萨斯大学奥斯汀分校举行。这次会议将有不同的演讲者，他们的工作以关键和重要的方式将标题中列出的主题联系在一起。会议的目标是向广泛的研究人员展示这些主题的相互联系，他们的工作可能不一定涉及每个领域，包括来自代表性不足群体的研究人员、职业生涯早期研究人员以及来自文科和R2大学的研究人员。会议的形式包括一个小时的全体研究演讲，多个闪电谈话会议，以及专门用于非正式数学讨论的时间。这次活动将推动来自不同数学领域和机构以及来自不同职业阶段的研究人员之间的新合作。会议将集中讨论几何拓扑学、几何群论、数论、表示论和谱几何之间的相互作用。这种相互作用的核心是李群及其离散子群的理论，在该理论中，人们可以通过离散群在相关齐次空间上的作用产生流形。特别有趣的是在双曲空间上等距作用的离散群。这些作用通过几何化在低维几何和拓扑学中起着基础性的作用，并为当前几何群论和几何结构形变理论的研究提供了动力。在更一般的单李群的离散子群中，算术格发挥着核心作用，它利用了代数/解析数论和代数群论的技术。这些相互作用在相关空间的几何和算术格的代数之间提供了深刻而重要的联系。一百多年来，所有这些相互作用推动了数学研究，这次会议将把来自这些领域和密切相关领域的研究人员聚集在一起，为未来寻找新的令人兴奋的联系。会议的网站位于https://sites.google.com/view/awr-conference/homeThis，该奖项反映了国家科学基金会的法定使命，并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，被认为值得支持。

A conference on Geometry, Arithmetic, and Groups organized by researchers from across the United States will be held at the University of Texas, Austin, June 20-24, 2022. This conference will feature a diverse mix of speakers whose work connects the topics listed in the title in crucial and important ways. The goal of the conference is to expose the inter-connectivity of these topics to a wide range of researchers whose work may not necessarily touch each of the areas, including researchers from underrepresented groups, early career researchers, and researchers from liberal arts and R2 universities. The format for the conference includes one hour plenary research talks, multiple lightning-talk sessions, and dedicated time for informal mathematical discussions. This event will provide the impetus for new collaborations between researchers from diverse mathematical fields and institutions, and from a wide variety of career stages.The conference will focus on the interactions between geometric topology, geometric group theory, number theory, representation theory, and spectral geometry. At the heart of this interplay is the theory of Lie groups and their discrete subgroups, where one can produce manifolds via the actions of discrete groups on associated homogeneous spaces. Of particular interest are discrete groups acting isometrically on hyperbolic space. These actions play a fundamental role in low dimensional geometry and topology via geometrization, and have provided the impetus for much current research in geometric group theory and the deformation theory of geometric structures. Among the discrete subgroups of simple Lie groups more generally, arithmetic lattices play a central role, utilizing technology from algebraic/analytic number theory and the theory of algebraic groups. These interactions provide deep and important connections between the geometry of the associated spaces and the algebra of the arithmetic lattices. All these interactions have driven mathematical research for more than one hundred years, and this conference will bring together researchers from these areas and closely related fields to search for new and exciting connections for the future. The website for the conference is at https://sites.google.com/view/awr-conference/homeThis 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.