Conference: Summer School on Discrete subgroups of Lie groups: Dynamics, Actions, Rigidity

This NSF award provides support for US based participants to attend the Conference: Summer School on Discrete Subgroups of Lie groups: Dynamics, Actions, Rigidity to be held July 7 to 18, 2025 at IHES in Bures-Sur-Yvette outside Paris. The primary goal of this Summer School is to allow researchers to come together and learn about recent breakthroughs and exciting developments in this area.

The Summer School will feature seven mini-courses on a variety of topics in discrete subgroups of Lie groups. Each mini-course will be organized into units of 2-3 hours of a lecture followed by a problem session. This will allow each lecturer to properly introduce their topic to non-experts, including graduate students and postdocs, and allow the participants to acquaint themselves in a reasonably detailed way with the techniques used to attack central problems.

The primary purpose of the award is to provide travel funding to students and scholars from the US to participate in the Summer School, so that they can learn about and participate in this exciting research area.

Rigidity properties of geometric and dynamical structures under either symmetry or extremality assumptions, e.g., on curvature or entropy, have been of great interest in both geometry and dynamics, and number theory for some time. The goal typically is to force such structures to be of classical, often algebraic nature. These ideas and results build on the celebrated works of Mostow, Prasad, Margulis and Zimmer.

At the heart lies the discovery that the Mostow–Margulis type rigidity results for discrete subgroups of semisimple Lie groups have far-reaching counterparts in geometry and dynamics. Investigations in this area are often spurred by the sudden emergence of or deepening of connections to other areas of mathematics. Recently, new developments have been occurring at lightning speed.

This school will highlight the remarkable progress on several important problems broadly centered around the study of discrete subgroups of Lie groups. The concentrated activity around this Summer School funded in part by this grant are crucial for capturing this momentum and spur further progress. Information about the Summer School can be found at the IHES website: https://indico.math.cnrs.fr/event/12324/

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.