Thermodynamic Formalism: CIRM Jean-Morlet Chair, Fall 2019

Part I Specification and Expansiveness.- Beyond Bowen's Specification Property.- The role of continuity and expansiveness on leo and periodic specification properties.- Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions.- Statistical properties of periodic points for infinitely renormalizable unimodal maps.- Part II Probability theory, ergodicity and thermodynamic formalism.- Recurrent sets for ergodic sums of an integer valued function.- Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations.- Limit theorem for reflected random walks.- The strong Borel-Cantelli property in conventional and nonconventional setups.- Application of the convergence of the spatio-temporal processes for visits to small sets.- Part III Geometry and thermodynamic formalism.- Rate of mixing for equilibrium states in negative curvature and trees.- Statistical properties of the Rauzy-Veech-Zorich map.- Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds.- Higher Teichmüller Theory for surface groups and shifts of finite type.- Part IV Fractal Geometry.- Dimension estimates for C1 iterated function systems and C1 repellers, a survey.- Intermediate dimensions - a survey.- Fractal geometry of Bedford-McMullen carpets.- Some variants of Orponen's theorem on visible parts of fractal sets.