Stationary Random Subgroups and Injectivity Radius in Negative Curvature

Explore the connections between stationary random subgroups and injectivity radius in negatively curved spaces in this 47-minute lecture by Ilya Gekhtman. Delve into the properties of non-free stationary actions of rank one simple Lie groups, examining how their stabilizers exhibit "large" characteristics. Learn about the application of random walk techniques to obtain a conditional rank one analogue of the Fraczyk-Gelander theorem in higher rank. Investigate the relationship between the bottom of the spectrum of the Laplacian on hyperbolic manifolds and the existence of points with arbitrarily large injectivity radius. Gain insights into related results for general isometry groups of proper geodesic Gromov hyperbolic spaces. All relevant concepts will be thoroughly explained during this mathematical exploration, which is part of the Measured Group Theory program at the Centre de recherches mathématiques.