Explore the intricate connections between homogeneous dynamics and recent developments in discrete subgroups of infinite volume within Lie groups through this comprehensive workshop series. Delve into cutting-edge research on Anosov representations and their generalizations, examining how geometric structures and dynamical systems interact in higher-rank settings. Learn from leading experts as they present foundational introductions to geometry and dynamics on semisimple Lie groups, followed by specialized topics including divisible convex sets, equidistribution of periodic tori, and local mixing of diagonal flows on Anosov homogeneous spaces. Investigate the geometric consequences of dynamics associated to Anosov representations, discover properties of discrete subgroups with finite Bowen-Margulis-Sullivan measures, and examine horospherically invariant measures with rank dichotomy for Anosov groups. Study advanced concepts such as u-Gibbs states in homogeneous dynamics, transverse groups, Thurston's asymmetric metrics, ghost polygons with Poisson brackets, and orbit counting theorems for cusped Hitchin representations. Gain insights into the bottom of the L² spectrum of higher-rank locally symmetric spaces and explore the rich interplay between geometric structures, representation theory, and dynamical systems in this specialized area of mathematics.

Syllabus

Jean-François Quint - 1/3 An Introduction to Geometry and Dynamics on Semisimple Lie Groups and (..)
Tengren Zhang - 1/3 Anosov Representations
Jean-François Quint - 2/3 An Introduction to Geometry and Dynamics on Semisimple Lie Groups and (..)
Pierre-Louis Blayac - Divisible Convex Sets with Properly Embedded Cones
Nguyen-Thi Dang - Equidistribution of Periodic Tori
Jean-François Quint - 3/3 An Introduction to Geometry and Dynamics on Semisimple Lie Groups and (..)
Tengren Zhang - 2/3 Anosov Representations
Pratyush Sarkar - Local Mixing of Diagonal Flows on Anosov Homogeneous Spaces
Sara Maloni - Geometric Structures Associated to Anosov Representations
Sam Edwards - The Bottom of the $L^2$ Spectrum of Higher-rank Locally Symmetric Spaces
Tengren Zhang - 3/3 Anosov Representations
Minju Lee - 1/2 Discrete Subgroups with Finite Bowen-Margulis-Sullivan Measure in Higher Rank
Andrés Sambarino - 1/2 Dynamics Associated to Anosov Representations: Some Geometric Consequences
Rafael Potrie - Homogeneous Dynamics and u-Gibbs States
Minju Lee - 2/2 Horospherically Invariant Measures and a Rank Dichotomy for Anosov Groups
Andrew Zimmer - Transverse Groups
Andrés Sambarino - 2/2 Dynamics Associated to Anosov Representations: Some Geometric Consequences
Leon Carvajales - Thurston's Asymmetric Metrics for Anosov Representations
François Labourie - Ghost Polygons, Poisson Bracket and Convexity
Giuseppe Martone - Orbit Counting Theorem for Cusped Hitchin Representations