Pathways Workshop: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups: Criterion for Finiteness of BMS Measure
Presenter
January 22, 2026
Keywords:
- low-dimensional topology
- geometric structures
- homogeneous dynamics
- Anosov representations
- Higher rank Lie groups
- symmetric spaces of non- compact type
MSC:
- 57M50 - General geometric structures on low-dimensional manifolds
- 57M60 - Group actions on manifolds and cell complexes in low dimensions
- 57N16 - Geometric structures on manifolds of high or arbitrary dimension
- 57S25 - Groups acting on specific manifolds
- 22E40 - Discrete subgroups of Lie groups
- 22F30 - Homogeneous spaces
- 37E05 - Dynamical systems involving maps of the interval
- 37E10 - Dynamical systems involving maps of the circle
- 37E30 - Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
- 37E35 - Flows on surfaces
- 30F60 - Teichmüller theory for Riemann surfaces
- 32G15 - Moduli of Riemann surfaces
- Teichmüller theory (complex-analytic aspects in several variables)]
- 30F40 - Kleinian groups (aspects of compact Riemann surfaces and uniformization)
Abstract
In many useful settings, having a finite BMS measure on a flow space allows people to normalize the BMS measure into a probability measure and facilitates powerful ergodic theoretic tools. This often leads to asymptotic estimates for counting orbital points and establishing equidistribution results. Hence, it is important to know when a dynamical system admits a finite BMS measure. In this talk, I will introduce the criterion for the finiteness of BMS measure on the unit tangent bundle of a negatively curved manifold introduced by Pit-Schapira. If time permits, I will also present my recent work that extends this criterion to the setting of discrete subgroups of higher rank semisimple Lie groups.