Conference: Groups Actions and Rigidity: Around the Zimmer Program

该NSF奖项为美国的参与者提供支持，以参加将于2024年4月至7月在马赛的国际数学会议中心和巴黎的亨利庞加莱研究所举行的一系列研讨会。这些研讨会与特殊学期集体行动和刚性：在此期间围绕IHP的Zimmer项目举行。 这两个研讨会和特别学期的目标是汇集专家工作在一个相关的集群的及时和重要的主题，在动力学和几何相关，大群体或空间的行动与大量的对称性。该奖项的主要目的是提供旅行资金，让来自美国的早期职业学者参加研讨会和学期计划。高度对称流形传统上在数学中发挥着核心作用，从数论到动力学再到几何。本研究课题围绕Zimmer和Gromov提出的一个研究具有大型对称群的流形的方案，其总体思想是这种流形应该产生于自然的代数和几何构造。在这一领域的调查往往是由突然发现或深化连接到其他领域的数学。最近新的事态发展以惊人的速度出现。 特别重要的是加深了连接到低维拓扑，齐次和双曲动力学以及新的连接到算子代数，并经典的工作之间的李群特征连接拓扑群。需要围绕这一特别术语开展集中活动，并由这笔赠款部分资助讲习班，以抓住这一势头，推动进一步的进展。有关个别研讨会和会议的信息可以在www.example.com上找到https://indico.math.cnrs.fr/event/9043/.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。

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.