Geometry, Arithmetic, and Groups.

几何、算术和群。

• 批准号: 2204684
• 负责人: Cameron Gordon
• 金额: $ 2万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-06-15 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204684&HistoricalAwards=false
• 关键词: Geometry; Arithmetic; Groups.

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.

由来自美国各地的研究人员组织的几何，算术和团体会议将于2022年6月20日至24日在德克萨斯大学奥斯汀分校举行。本次会议将以各种各样的发言者为特色，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起来。会议的目标是将这些主题的相互联系暴露给广泛的研究人员，他们的工作可能不一定触及每个领域，包括来自代表性不足的群体的研究人员，早期职业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会谈，多个闪电谈话会议，以及专门的时间进行非正式的数学讨论。 本次会议将为来自不同数学领域和机构的研究人员以及来自各种职业阶段的研究人员之间的新合作提供动力。会议将重点关注几何拓扑学，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，其中可以通过离散群在相关齐性空间上的作用来产生流形。特别感兴趣的是等距作用于双曲空间的离散群。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的变形理论的许多研究提供了动力。在简单李群的离散子群中，算术格发挥了核心作用，利用代数/解析数论和代数群理论的技术。这些相互作用在相关空间的几何学和算术格的代数学之间提供了深刻而重要的联系。所有这些相互作用推动了一百多年的数学研究，这次会议将汇集来自这些领域和密切相关领域的研究人员，为未来寻找新的和令人兴奋的联系。 会议的网站是https://sites.google.com/view/awr-conference/homeThis奖反映了NSF的法定使命，并已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的支持。