Conference: Groups Actions and Rigidity: Around the Zimmer Program

该NSF奖为美国参与者提供了参加一系列研讨会的支持，这些研讨会将于2024年4月至7月在马赛的国际Rencontres数学中心和巴黎的Henri Poincare研究所举行。在此期间，这些研讨会将与一个特别学期的小组行动和刚性：围绕IHP的齐默项目举行。研讨会和特别学期的目标都是汇集在动力学和几何相关的及时和重要主题的相关集群中的专家，与大量对称的群体或空间的行动有关。该奖项的主要目的是为来自美国的早期职业学者提供旅行资金，以参加研讨会和学期计划。高度对称流形传统上在数学中扮演着中心角色，从数论到动力学再到几何。本课题以Zimmer和Gromov提出的研究具有大群对称的流形的方案为中心，其一般思想是这样的流形应该产生于自然的代数和几何结构。这一领域的研究往往是由突然发现或加深与数学其他领域的联系所激发的。最近的新发展正以惊人的速度发生。特别重要的是加深了与低维拓扑的联系，与齐次和双曲动力学的联系，以及与算子代数的新联系，以及与连通拓扑群中李群表征的经典工作的联系。需要围绕这一特别期限开展集中活动以及部分由这笔赠款资助的讲习班，以抓住这一势头并推动进一步进展。关于个别研讨会和会议的信息可以在https://indico.math.cnrs.fr/event/9043/.This上找到，奖项反映了NSF的法定使命，并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，被认为值得支持。

This NSF award provides support for US based participants to attend a sequence of workshops, to be held at Centre Internationale de Rencontres mathematique in Marseilles and the Insitut Henri Poincare in Paris in April-July 2024. These workshops are held in conjunction with a special semester Group actions and Rigidity: Around the Zimmer Program at IHP during this period. The goal of both the workshops and special semester are to bring together specialists working in a related cluster of timely and important topics in dynamics and geometry related to, actions of large groups or spaces with lots of symmetries. The primary purpose of the award is to provide travel funding to allow early career scholars from the US to participate in the workshops and the semester program.Highly symmetric manifolds traditionally play a central role in mathematics, ranging from number theory to dynamics to geometry. This research topic centers on a program put forward by Zimmer and Gromov to study manifolds with large groups of symmetries, with the general idea that such manifolds should arise from natural algebraic and geometric constructions. Investigations in this area are often spurred by sudden discovery of or deepening of connections to other areas of mathematics. Recent new developments have been occurring with breakneck speed. Particularly important have been deepening connections to low dimensional topology, to homogeneous and hyperbolic dynamics as well as novel connections to operator algebras, and to classical work on characterizations of Lie groups among connected topological groups. The concentrated activity around this special term and the workshops funded in part by this grant are needed to capture this momentum and spur further progress. Information about individual workshops and meetings can be found at https://indico.math.cnrs.fr/event/9043/.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.