Sixth Framework Programme

Marie Curie Actions

 

EU Research Training Network CODY

Conformal Structures and Dynamics

Research Training Networks
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Teamss

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Leader: Michel Zinsmeister (click here for the address of MAPMO)

The Orleans team is part of the laboratory “MAPMO” (UMR 6628) which has recently merged with the mathematics laboratory of the University of Tours to form the “Fédération Denis Poisson”, one of the biggest CNRS-associated mathematical laboratory in France. This laboratory has a strong group in dynamical systems, with a large spectrum of themes: ergodic theory and geometry, fractal and multifractal analysis, holomorphic dynamics and mathematical physics. It has about 40 PhD students and hosts many postdocs (including from different EEC RTN contracts). This team was one of the leading teams of HCM contract ERB CHRX CT92 0071, and has a long tradition of organisation of conferences, summer schools and all kind of events. The geographical central position of Orleans allows moreover to optimise its interaction with the other participants of the team who are spread around France (Paris, Marseille, Toulouse, Rennes, Lille, Clermont Ferrant). All these centres have a long tradition of cooperation through different existing French or European networks such as

  • Grefi-Mefi, a Franco-Italian reearch group (GDR).
  • Polynomial Dynamics, an ACI (network of young researchers) run by Serge Cantat (Rennes) and involving Marseille, Toulouse and Paris 6.
  • GDR Theorie ergodique et systemes dynamiques involving all the quoted centers.

Principal researchers for this project:
Michel Zinsmeister: Professor (Université d'Orléans). Team coordinator. Expert in Geometric Function Theory, especially Hausdorff dimension of Julia sets, thermodynamic formalism. (50%)
Viviane Baladi: Researcher. Institut de Mathematique de Jussieu, Université Paris 7. Invited speaker at ECM, Barcelona 2000. In editorial boards of Ann. Sc. ENS, ETDS, Ann IHP physic theor. Expert in dynamical zeta functions and dynamical spectrum: spectrum of the transfer operator in non uniformly hyperbolic settings, small random perturbations, extension of the Milnor-Thurston kneading theory in higher dimensions; SRB measures and spectrum of coupled map lattices, anisotropic spaces of distributions and dynamics". (20%)
Artur Avila: Researcher, Dynamical systems, Statistical properties of unimodal maps, ergodic properties of interval exchange maps and Teichmueller flows, spectrum of Schroedinger operator. (15%)
Jérôme Buzzi: Researcher (École Polytechnique).Studies of various complexities and their interplay with dynamical properties such as semi-uniform hyperbolicity - the study of complexity itself (through measures with maximum entropy --- e.g. for entropy-expanding maps) as well as classical issues like absolutely continuous invariant measures and thermodynamic formalism . (15%)
Guy David: Professor (Université Paris-Sud, Orsay). Invited speaker at ICM, Berkeley 1986, Salem prize 1987, IBM-France prize 1990. His work with S. Semmes (invited speaker at ICM, Z¸rich 1994) has received international recognition. Expert in harmonic analysis, singular integral operators; geometric measure theory: uniformly rectifiable sets; image processing: minimizers of Mumford-Shah functional. (5%)
Volker Mayer: (MaÓtre de ConfÈrences, Université de Lille 1) Quasiconformal Analysis, Iteration of meromorphic functions. (15%)
Bertrand Duplantier: Researcher (CEA – Saclay). Expert in Conformal Field Theory and more specially in scaling limits of various discrete models of statistical mechanics where he has major contributions. (20%)
Jacek Graczyk: Professor (Université Paris-Sud, Orsay). Expert on geometric and measure theoretic aspects of non hyperbolic dynamical systems in real or complex dimension 1. (10%)
Pierre Pansu: Professor (Université Paris-Sud, Orsay). Expert in Riemannian geometry: isoperimetric inequalities; analysis on Carnot groups; geometric group theory: rigidity of symmetric spaces. (20%)
Jean-Christophe Yoccoz (Collège de France). Salem Prize 1988, Fields medalist 1994. Expert in non uniformly hyperbolic dynamics; one-dimensional dynamics over the reals, complex and p-adic numbers; KAM theory, small divisors; recent interests include lemmings population models. (10%)
Tan Lei: Maître de Confèrences (Université de Cergy-Pontoise). Expert in iterations of rational maps, more particularly: the topology and geometry of the the unstable phases (the Julia set), their counterpart in the parameter space, and realisations of systems with given combinatorics. (20%).
Claude Tricot: Professor (Université de Clermont-Ferrant). Expert in multifractal analysis and Dimension Theory. (20%)
Anton Zorich: Professor (Université de Rennes 1). ICM talk 2006. Expert in geometry and topology of the moduli spaces of quadratic differentials, in Teichmuller geodesic flow, in geometry and dynamics of translation surfaces and of measured foliations. (10%)
Vincent Beffara (Researcher, CNRS UMR 5669 at ENS-Lyon), expert on random walks and SLE. (15%)
Xavier Buff (Université Paul Sabatier, Toulouse). MaÓtre de ConfÈrences. Holomorphic dynamics: boundaries of Siegel discs, renormalization. (20%)
Arnaud Chéritat† (Université Paul Sabatier, Toulouse). MaÓtre de ConfÈrences. Holomorphic dynamics: boundaries of Siegel discs, renormalization. (20%)
Sébastien Ferenczi
: researcher, CNRS, Institut de MathÈmatiques de Luminy, Marseille. Expert on interactions between dynamical systems, arithmetic, and word combinatorics. (30%)
Julien Barral: researcher, INRIA, expert in fractal and multifractal analysis, multiplicative cascades. (10%).
Bernard Sapoval: Directeur de recherchÈ, CNRS, Ecole Polytechnique, Laboratoire de Physique de la MatiËre CondensÈ. Expert on physics of fractals and irregular systems. Extensive industrial collaborations with COLAS SA (sound waves on roads) and others. (15%)

Associate researchers: A.Batakis, S.Cantat, M. Bauer, D. Bernard, M. Bourdon, A. Douady, M. Peigne, P. Flajolet, H-H. Rugh, Y. Heurteaux, R. Perez- Marco, P. Arnoux, X. Bressaud, P. Haissinsky, J. Hubbard, P. Hubert, S. Vaienti, K. Gawedski, M. Peigne, S.Tcheremchantsev, S. Crovisier.

Selected Publications:
B.Duplantier: Conformal Fractal Geometry and Boundary Quantum Gravity. Proceedings of Symposia in Pure Mathematics, 72-2, 2004.
X.Buff, A.ChÈritat†: Ensembles de Julia quadratiques de mesure strictement positive. CRAS Paris, 341, dÈcembre 2005.
A.Avila, C. G. Moreira†: Statistical properties of unimodal maps: physical measures, periodic points and pathological laminations. Publications MathÈmatiques de l'IHÉS 101 (2005), 1-67.