Conference: Groups Actions and Rigidity: Around the Zimmer Program

William Marsh Rice University, Houston TX

Investigators

Abstract

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.