Conference: I.H.E.S. Workshop: Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups

会议：I.H.E.S.

• 批准号: 2321093
• 负责人: Richard Canary
• 金额: $ 4万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-06-15 至 2024-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2321093&HistoricalAwards=false
• 关键词: Conference; I.H.E.S.; Workshop; Homogeneous; Dynamics

Funding for this award will support US participants at a workshop on ``Homogeneous Dynamics and Geometry in Higher-Rank Lie Group'' to be held June 19--23, 2023, at Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette, France. The aim of the workshop is to bring together two intellectual communities that have recently made significant advances in the study of discrete subgroups of higher rank semi-simple Lie groups: the homogeneous dynamics community and the higher rank Teichmuller theory community. The event is timely, since techniques from homogenous dynamics are becoming increasingly prominent in the study of discrete subgroups of Lie groups in both fields. Each morning there will be two mini-course lectures, intended to introduce researchers to techniques from both fields, while the afternoon will be devoted to research lectures. Bringing together these two groups will lead to further interactions and will accelerate development in these exciting areas. The organizers are committed to funding a diverse group of mathematicians.Homogeneous dynamics deals with flows on the quotients of Lie groups by discrete subgroups. There is a well-developed, now classical, study of orbit closures, measure classifications, counting and equidistribution results in homogeneous spaces of semisimple Lie groups of finite volume, i.e. when the discrete subgroup is a lattice. These ideas have had many applications in seemingly unrelated areas, for example, the solutions of the Oppenheim and Littlewood conjectures in number theory, and more recently in Teichmuller dynamics. In the last decade, there has been significant progress in extending this theory to study discrete subgroups of rank one Lie groups which are not lattices. The fundamental tool in this work is the theory of Patterson-Sullivan measures associated to actions of discrete subgroups on the geometric boundaries of hyperbolic spaces. The time is ripe for the pursuit of generalizations of these works to higher rank homogeneous spaces of infinite co-volume. This theory has already seen exciting preliminary development in the context of Anosov representations.Further details about the workshop, including a full list of speakers, are available at the conference website: https://indico.math.cnrs.fr/event/8759/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.

该奖项的资金将在2023年6月19日至23日在法国Bures-Sur-Serudifiques Institut des Scientifiques举行的“高级谎言组的同质动力和几何形状”研讨会上为我们的参与者提供支持。研讨会的目的是汇集两个最近在研究高级半简单谎言群体的离散亚组的知识社区：同质动力学界和高级Teichmuller理论社区。 该事件是及时的，因为在研究两个领域的谎言组的离散亚组中，同质动力学的技术变得越来越突出。每天早晨，将有两个小型课程讲座，旨在向研究人员介绍两个领域的技术，而下午将致力于研究讲座。汇集这两个小组将导致进一步的互动，并在这些令人兴奋的领域加速发展。 组织者致力于资助一组多样化的数学家。均匀的动态处理通过离散亚组在Lie组的商中的流动。有一个完善的，现在是经典的，对轨道封闭，测量分类，计数和等分分配的研究导致有限体积的半密布谎言组的同质空间，即当离散亚组是晶格时。这些想法在看似无关的领域中有许多应用，例如，在数字理论中，Oppenheim和Littlewood猜想的解决方案以及最近在Teichmuller Dynamics中。 在过去的十年中，扩展该理论来研究排名一组不是晶格的谎言组的离散亚组取得了重大进展。这项工作的基本工具是与离散亚组对双曲线空间几何边界的作用相关的帕特森·苏利文措施的理论。当这些作品概括到无限卷积的较高统一空间的概括中，时间已经成熟。 该理论已经在Anosov代表的背景下看到了令人兴奋的初步发展。有关研讨会的详细信息，包括完整的演讲者列表，可以在会议网站：https：//indico.cnrs.fr/event/87759/87759/87759/这一奖项中均反映了NSF的法定任务和范围的范围。