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