ANR Dynacomplexe
Année 2007/2008

1) Cours:

Y. Pesin
(Pennsylvania State University)
"Dimension Theory in View of Dynamical Systems."

Premier Cours: Lundi 1 Octobre à 14h00 salle 113-115:
Dimension characteristics of sets and measures (Hausdorff dimension, box dimension, etc.). General Caratheodory characteristics.

Deuxième Cours: Vendredi 5 Octobre à 10h00 salle 113-115:
Application of the Caratheodory construction to dynamical systems I: correlation dimension, Hentshel-Procaccia spectrum for dimensions. Multifractal formalism for dynamical systems.

Troisième Cours: Vendredi 12 Octobre à 10h00 salle 113-115:
Application of the generalized Caratheodory construction to dynamical systems II: topological entropy, topological pressure, and Kolmogorov-Sinai metric entropy as dimension-like chracteristics.

2) Groupe de Travail "Dynamique et Géométrie Complexes":

Mercredi 24 Octobre à 14h30 salle 117-119:
 Charles Favre (Paris 7)
"Compactification des applications polynomiales de C^2."

Mercredi 7 Novembre à 14h30 salle 117-119:
 Gabriel Vigny (Orsay)

"Transformée de Lelong-Skoda et inégalités d'auto-intersection dans les variétés kählériennes compactes."

Mercredi 28 Novembre à 14h30 salle 117-119:
Slawomir Kolodziej (Cracovie)
"Stability and Hölder continuity of solutions to the complex Monge-Ampère equation with the right hand side in L^p."

Mercredi 5 Décembre à 14h30 salle 117-119:
Benoît Saussol (Université de Bretagne Occidentale)
"Grandes déviations pour les temps de retour successifs."

Mercredi 12 Décembre à 14h30 salle 117-119:
Christophe Dupont (Orsay)
"Codage et théorème central limite singulier pour les endomorphismes de CP(k)."

Mercredi 9 Janvier à 14h30 salle 117-119:
Benoît Claudon (Université de Nancy)
"Gamma-réduction des variétés et orbifoldes kählériennes compactes."

Mercredi 9 Janvier à 16h00 salle 117-119:
Tomoki Kawahira (Nagoya University)
"Degeneration and bifurcation on the Lyubich-Minsky 3-laminations of quadratic maps (in view of analogy to quasiFuchsian group and Bers slice)."

Mercredi 19 Mars à 16h00 salle 117-119:
Dror Varolin (Stony Brook)
"Basepoints of the pluricanonical ring"

Mercredi 26 Mars à 16h00 salle 117-119:
Yusuke Okuyama (Kyoto)
"Nevanlinna theoretical order estimate of equidistribution in complex dynamics"

Mercredi 9 Avril à 16h00 salle 117-119
Robert Berman (Institut Fourier)
"Un principe variationnel pour les mesures d'équilibre."

Mercredi 11 Juin à 16h00 salle 117-119
Gabriele La Nave (Yeshiva University NYC)
"Twisted Einstein metrics and Kahler-Ricci flow."

3) Journées Dynamique et Géométrie Complexes le jeudi 5 et Vendredi 6 Juin à Chevaleret:

Jeudi à 15h00: J.-H. Keum (Korea Inst. Adv. Study)
Automorphisms of K3 surfaces

This is a survey on how to compute the automorphism group of a K3 surface.
More precisely, we will explain how to find geometric generators of  
the automorphism group, using the geometry of Leech lattice.
This idea, originally due to Shigeyuki Kondo, has been successful
in the case of some interesing K3 surfaces such as Jacobian Kummer surfaces,
Kummer surfaces of product type, and Hessian surface of a cubic surface.

Jeudi à 16h30 : S. Kondo  (Nagoya University)
Finite non-symplectic automorphisms of K3 surfaces and moduli

I shall give a survey on recent progress of classification of
finite nob-symplectic automorphisms of K3 surfaces.  Moreover
I shall discuss on moduli of pairs of a K3 surface and a finite
non-symplectic automorphism.

Vendredi à 9h30 : H. de Thélin  (Orsay)
Dynamics of meromorphic maps I : entropy and Lyapounov exponents

Vendredi à 11h : G. Vigny (Orsay)
Dynamics of meromorphic maps II : the case of birational maps of CP^k

Vendredi à 14h : M. Hindry (IMJ)
Systèmes dynamiques arithmétiques, quelques aspects

Vendredi à 15h30 : N. Sibony (Orsay)
Super-Potentials on Compact Kähler manifolds and dynamics of automorphisms

In this joint work with T.-C. Dinh, we introduce a notion of super-potential
(canonical function) associated to positive closed (p,p)-currents on compact
Kähler manifolds and we develop a calculus on such currents.
One of the key points in our study is the use of deformations in the space of
currents. As an application, we obtain several results on the dynamics
of holomorphic automorphisms : regularity and uniqueness of the Green  
We show in particular that some cohomology classes contain only one
positive closed (p,p)-current. We also get the regularity, the  
entropy, the ergodicity and the hyperbolicity of the equilibrium  

Vendredi à 17h : K. Oguiso (Keio University)
Mordell-Weil groups of fibered hyperkähler manifolds and applications

 From the complex dynamical view or lattice theoretical view,
one can show that almost abelian subgroups of the birational automorphism
group of a projective hyperkaehler manifold is of rank less than or
equal to ${\rm Max} (1, \rho(X) -2)$. The aim of my talk is the following:

1) Compare this estimate with the rank of the Mordell-Weil group, i.e.,
subgroup of birational automorphisms arizing from rational sections of

2) Show one way to produce non-commutative free subgroups of  
birational automorphisms via Mordell-Weil groups.