Speaker: Rémi Coulon (CNRS, Dijon)
Title: Ergodic theory in groups with a contracting element
Abstract: Ergodic theory has proven to be a powerful tool for studying negatively curved Riemannian manifolds and their fundamental groups. For instance, the seminal work of Margulis extracts from the mixing of the geodesic flow precise asymptotics for the number of closed geodesics of a given length. This approach has been extended beyond the realm of manifolds, e.g., to CAT(-1) spaces and CAT(0) spaces with a rank-one element. This talk will report on an ongoing project whose goal is to carry (some of) these tools to the context of geometric group theory: given a general metric space X with a weak form of negative curvature (captured by the existence of a contracting element in its isometry group), we will explain how to build a geodesic flow on X and investigate its dynamical properties, such as ergodicity and mixing.
This is joint work with Samuel Tapie.
Speaker: Natalia Jurga (St Andrews University)
Title: Quantitative covering and equidistribution
Abstract: One of the fundamental features of an ergodic dynamical system (T,X,m) with supp(m)=X is that for almost every x in X, the orbit of x is dense in X and the sequence of empirical distributions along its orbit converges to the measure m. In this talk we will discuss quantitative versions of these facts and their connections to the fractal properties of the measure m. This is based on upcoming work with Mike Todd.
Speaker: Maryam Hosseini (City St George's, University of London)
Title: Some algebraic aspects of topological factoring
Abstract: Every zero-dimensional dynamical system can be expressed as an inverse limit of subshifts. This characterization was initially developed for Cantor minimal systems by I. Putnam et al. (1989,1992), linking them to C*-algebras and dimension groups, and later extended to all zero-dimensional systems by T. Shimomura (2021). E. Glasner in joint works with B. Wiess and B. Host explored the relationship between topological factoring of Cantor minimal systems and dimension groups (1995, 2012). In this talk, I will discuss about the generalization of these results to zero-dimensional dynamical systems by using the inverse limit realizations.
