Conference: Groups Actions and Rigidity: Around the Zimmer Program

该NSF奖项支持美国的参与者参加一系列研讨会，这些研讨会将于2024年4月至7月在马赛的国际数学中心和巴黎的亨利·庞加莱研究所举行。这些讲习班是与国际水文计划在此期间围绕齐默计划举办的一个特别学期联合举办的：集体行动和僵化。工作坊和特别学期的目标都是将相关的专家聚集在一起，这些专家工作在与大群体或具有大量对称性的空间的行动有关的动力学和几何方面的及时和重要的主题。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。高度对称的流形传统上在数学中扮演着核心角色，从数论到动力学再到几何。这项研究的主题集中在Zimmer和Gromov提出的研究具有大对称群的流形的程序上，一般的想法是这种流形应该来自自然的代数和几何构造。这一领域的研究往往是由于突然发现或加深了与其他数学领域的联系而引起的。最近的新发展正在以惊人的速度发生。尤其重要的是加深了与低维拓扑、齐次和双曲动力学的联系，以及与算子代数的新联系，以及关于连通拓扑群中李群的刻画的经典工作。需要围绕这一特别期限集中开展活动，并举办部分由这笔赠款资助的讲习班，以抓住这一势头并推动取得进一步进展。有关个别研讨会和会议的信息可在https://indico.math.cnrs.fr/event/9043/.This奖上找到，该奖项反映了国家科学基金会的法定使命，并通过使用基金会的智力优势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.