

List of courses There will be 6 courses on different aspects of dynamical systems: Benoist Yves (3h): Recurrence on homogeneous space. Abstract: In this course I will focus on recurrence properties for random walks on finite volume homogeneous spaces. I will explain EskinMargulis approach and how the use of the highest weight theory allows to extend it to more general situations. If time permits, I will also describe other dynamical systems for which the nonescape of mass property is a crucial issue. Foulon Patrick (1h30): Entropy of convex real projective structures. Abstract: We will present some results about the dynamics of real projectives structures in the compact cases such as the Anosov property, Crampon's inequality for topological entropy, Liapunov exponents and finally investigate SRB entropy. Paulin Frédéric (3h): Hyperbolic geometry and ergodic methods. Application to arithmetics. Abstract: I will survey tools (BowenMargulis and Gibbs measures, skinning measures) and methods (mixing and equidistribution properties) of the ergodic theory of the geodesic flow of negatively curved manifolds, in order to study various arithmetic applications (geometric Diophantine approximation, counting and equidistribution of arithmetically defined points, ...). Quint Jean François (3h): Dynamics on homogeneous space: Abstract: Dans ce cours, je montrerai que SL_d(Z) est un réseau de SL_d(R), j'expliquerai le théorème de Borel et HarishChandra qui décrit dans quels cas G(Z) est un réseau dans G(R) et je présenterai le théorème de HoweMoore qui implique, par exemple, le mélange des flots géodésique des variétés hyperboliques de volume fini. RodriguezHertz Federico (3h): Smooth and measure rigidity of hyperbolic lattice actions. Abstract: In this series of lectures I plan to develop the theory of hyperbolic lattice actions on tori that we have pushed with A. Brown and Z. Wang. My plan is to restrict to the simplest case while explaining the main ingredients in this theory. Its aim is the classification of actions on tori whose homotopy data is hyperbolic even without assumption of invariant measure. Schapira Barbara (3h): Horocyclic flows on hyperbolic surfacess. Abstract: I will present results on the dynamics of horocyclic flows on the unit tangent bundle of hyperbolic surfaces, density and equidistribution properties in particular. I will focus on infinite volume hyperbolic surfaces. My aim is to show how these properties are related to dynamical properties of geodesic flows, as product structure, ergodicity, mixing, ...
Notes de cours: http://www.lamfa.upicardie.fr/schapira/recherche/CIRM.pdf
There will be also several lectures of 45 minutes: Pesin Yakov: Thermodynamics of towers of hyperbolic type and the liftability problem. Pollicott Mark: Dynamical definitions of the WeilPetersson metric on moduli space. Prikhodko Sasha: Dynamical system constructions of measures of Salem type. Abstract: We study a class of ergodic group actions with invariant probability measure providing spectral measures of Salem type. A distribution on a dual group is called Salem if the Fourier coefficients decay, in polynomial scale, exactly as t^{d/2}, and each function with a faster polynomial decay is square summable. We focus on existence of spectral measuress of Salem type, and after we discuss different properties as well as open questions concerning this new class of dynamical systems.
Qiu Yanqi: Scaling limits for ChristoffelDarboux kernels associated with some modified Jacobi's orthogonal polynomial ensembles. Abstract: We investigate the scaling limits for the modified Jacobi orthogonal polynomial ensembles. Explicit scaling limits for the ChristoffelDarboux kernels are obtained, the limit kernels are related to the ergodic decomposition of infinite Pickrell measures. This is a joint work with Alexander Bufetov.
Organising Committee
Posters Here is the list of posters (to be completed):
Important dates The registration is now closed. The list of participants can be found here: http://www.cirm.univmrs.fr/index.html/spip.php?rubrique2&EX=info_rencontre&annee=2014&id_renc=1129 Scientific committee Forni Giovanni Hasselblatt Boris Masur Howard Olshanski Grigori Goal of the school The main aim of the school will be to introduce young researchers to current developments in the geometric theory of dynamical systems. The first edition of the school has taken place at the ICTP in Trieste in June 2013. During the school there will be five courses of 3 hours and 7 talks of one hour. The school will take place close to Marseille, in CIRM The centerpiece of this school are 5 courses by mathematicians at the The school is related to the Chaire Morlet, at CIRM, which will be given to Boris Hasselblatt for 20132014, see http://www. Chaire Jean Morlet.
