Conference: I.H.E.S. Workshop: Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Funding for this award will support US participants at a workshop on ``Homogeneous Dynamics and Geometry in Higher-Rank Lie Group'' to be held June 19--23, 2023, at Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette, France. The aim of the workshop is to bring together two intellectual communities that have recently made significant advances in the study of discrete subgroups of higher rank semi-simple Lie groups: the homogeneous dynamics community and the higher rank Teichmuller theory community. The event is timely, since techniques from homogenous dynamics are becoming increasingly prominent in the study of discrete subgroups of Lie groups in both fields. Each morning there will be two mini-course lectures, intended to introduce researchers to techniques from both fields, while the afternoon will be devoted to research lectures. Bringing together these two groups will lead to further interactions and will accelerate development in these exciting areas. The organizers are committed to funding a diverse group of mathematicians. Homogeneous dynamics deals with flows on the quotients of Lie groups by discrete subgroups. There is a well-developed, now classical, study of orbit closures, measure classifications, counting and equidistribution results in homogeneous spaces of semisimple Lie groups of finite volume, i.e. when the discrete subgroup is a lattice. These ideas have had many applications in seemingly unrelated areas, for example, the solutions of the Oppenheim and Littlewood conjectures in number theory, and more recently in Teichmuller dynamics. In the last decade, there has been significant progress in extending this theory to study discrete subgroups of rank one Lie groups which are not lattices. The fundamental tool in this work is the theory of Patterson-Sullivan measures associated to actions of discrete subgroups on the geometric boundaries of hyperbolic spaces. The time is ripe for the pursuit of generalizations of these works to higher rank homogeneous spaces of infinite co-volume. This theory has already seen exciting preliminary development in the context of Anosov representations. Further details about the workshop, including a full list of speakers, are available at the conference website: https://indico.math.cnrs.fr/event/8759/ 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.