Reference number : GC-2017-Q1-03322, amendment number : , agreement type : G, recipient legal name : Tiozzo, Giulio (University of Toronto), recipient country : CA, recipient province : nan, recipient city : Ontario, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : The goal of this project is to investigate dynamical properties of low-dimensional systems using methods from ergodic theory. 
In particular, I will develop the theory of core entropy of polynomials as recently introduced by W. Thurston. Properties of this function will be related to the geometry and topology of the Mandelbrot set, and will be used to better understand the geometry of the parameter space of polynomials of higher degree and rational maps. 
Moreover, I will investigate the ergodic theory of random walks on groups acting on spaces with hyperbolic properties, and derive applications to geometric group theory, Teichmueller dynamics and low-dimensional topology. This will extend the theory of random walks on Lie groups, 
as developed by Furstenberg, Margulis, Zimmer, and others, to groups of interest in geometry and topology such as the mapping class group and the group of outer automorphisms of the free group., program purpose french : The goal of this project is to investigate dynamical properties of low-dimensional systems using methods from ergodic theory. 
In particular, I will develop the theory of core entropy of polynomials as recently introduced by W. Thurston. Properties of this function will be related to the geometry and topology of the Mandelbrot set, and will be used to better understand the geometry of the parameter space of polynomials of higher degree and rational maps. 
Moreover, I will investigate the ergodic theory of random walks on groups acting on spaces with hyperbolic properties, and derive applications to geometric group theory, Teichmueller dynamics and low-dimensional topology. This will extend the theory of random walks on Lie groups, 
as developed by Furstenberg, Margulis, Zimmer, and others, to groups of interest in geometry and topology such as the mapping class group and the group of outer automorphisms of the free group., agreement title english : Ergodic theory of low-dimensional dynamical systems, agreement title french : Ergodic theory of low-dimensional dynamical systems, agreement number : RGPIN, agreement value : 125000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada