31 Mar-4 Apr 2014 Marseille (France)

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 Eskin-Margulis 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 non-escape 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 (Bowen-Margulis 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 Harish-Chandra qui décrit dans quels cas G(Z) est un réseau dans G(R) et je présenterai le théorème de Howe-Moore qui implique, par exemple, le mélange des flots géodésique des variétés hyperboliques de volume fini.

 Rodriguez-Hertz 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.u-picardie.fr/schapira/recherche/CIRM.pdf


There will be also several lectures of 45 minutes:

Pesin YakovThermodynamics of towers of hyperbolic type and the liftability problem. 

Pollicott Mark:  Dynamical definitions of the Weil-Petersson metric on moduli space.

Prikhodko SashaDynamical 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 Christoffel-Darboux 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 Christoffel-Darboux 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

  • Bédaride Nicolas
  • Bufetov Alexander
  • Duchin Moon
  • Hubert Pascal
  • Rodriguez Hertz Federico


Here is the list of posters (to be completed):

  • Avdeeva Maria: "Generalized Erd\"os-Kac Theorems".
  • Bray Sarah: "The Dynamics of Hilbert Geometries". 
  • Emme Jordan: "Spectral measure for substitutive tilings".
  • Fougeron Charles: "TBA"
  • Gekhtman Ilya: "Pointwise ergodic averages and stable type of the mapping class group and some relatively hyperbolic groups".
  • Ghazouani Sellim: "Dynamics of the mapping class group on Aff(C)-characters".
  • Karpel Olena: "Subdiagrams and invariant measures of Bratteli diagrams."
  • Klimenko Alexey: "Asymptotic properties of Arnold tongues and Josephson effect."
  • Komech Sergey: " A geometric approach to the entropy and its adaptation to shape recognition".
  • Pecastaing Vincent:"Local homogeneity of rigid geometric structures."
  • Romaskevich Olga: " On the incenters of triangular orbits in elliptic billiards".
  • Taran Alexander: " Attractors generated by substitution systems".
  • Zimmer Andew: "Rigidity of complex convex divisible sets." 
  • Zubov Dmitry: " Cohomological equations for suspension flows over Vershik automorphisms".



Important dates

The registration is now closed. The list of participants can be found here:


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
forefront of research at the interface of Geometry and Dynamics. These will
provide a foundation for students starting research on related topics, and
they will provide a boost and guidance to students and post-doctoral
researchers already at work in this area or a related one.

The lecturers (Benoist, Foulon, Paulin, Quint, Rodriguez Hertz, Schapira)
are matched to complement each other in order to provide a broad picture of
the research landscape and the connections between various parts of it.
Their range of expertise is quite distinct but has substantial overlaps.

They have also been chosen with attention to their ability and inclination
to mentor students, and most of the organizing and scientific committee
members will participate as mentors to the young mathematicians, as will
other senior mathematicians.

The schedule allows ample time for informal interaction at the institute or
on the walk (20 minutes in the institute park and a national park) to the
nearby limestone cliffs on the Mediterranean
This allows not only for learning from presenters, mentors and peers, but
for collaborations on ongoing or new projects. 

The school is related to the Chaire Morlet, at CIRM, which will be given to Boris Hasselblatt for 2013-2014, see http://wwwChaire Jean Morlet.


Online user: 1