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

该奖项的资金将支持美国参与者参加将于2023年6月19日至23日在法国布雷斯-苏尔-伊维特高等科学研究所举行的“高阶李群中的齐次动力学和几何”研讨会。该研讨会的目的是汇集两个知识界，最近取得了显着进展，在研究离散子群的高阶半单李群：齐次动力学社区和高阶Teichmuller理论社区。 这一事件是及时的，因为齐次动力学的技术在这两个领域的李群离散子群的研究中变得越来越突出。每天上午将有两个迷你课程讲座，旨在向研究人员介绍这两个领域的技术，而下午将专门用于研究讲座。将这两个群体聚集在一起将导致进一步的互动，并将加速这些令人兴奋的领域的发展。 组织者致力于资助一个不同的数学家团体。齐次动力学处理离散子群的李群的等价物上的流动。有一个发达的，现在经典的，研究轨道封闭，措施分类，计数和equidistribution结果在齐性空间的半单李群的有限体积，即当离散子群是一个格。这些想法在看似无关的领域有许多应用，例如，数论中的奥本海姆和利特尔伍德定理的解，以及最近的泰希穆勒动力学。 在过去的十年中，有显着的进展，扩大这一理论研究离散子群的秩一李群，而不是格。在这项工作中的基本工具是与双曲空间的几何边界上的离散子群的行动相关的Patterson-Sullivan措施理论。时机已经成熟的追求推广这些作品更高的秩齐性空间的无限合作体积。 这个理论已经在Anosov的陈述中得到了令人兴奋的初步发展。关于研讨会的更多细节，包括演讲者的完整名单，可以在会议网站上找到：https://indico.math.cnrs.fr/event/8759/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。

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.