twitter  twitter
  • 5 minutes Lebesgue
    26 sep 2017

    Les vidéos des exposés seront mises en ligne quelques jours après l'exposé. Vidéothèque

    Prochain exposé :

    26-09-2017Roger Lewandowski
    N raisons d'adhérer à la SMAI où N tend vers l'infini

    Lieu

    Rennes

    Exposés à venir:

    10-10-2017:  Présentation des Annales Henri Lebesgue

    17-10-2017:  Rémi Coulon

    07-11-2017:  Guy Casale

    21-11-2017:  Marine Fontaine

  • Conférence - Analyse géométrique à Roscoff
    9 oct 2017 - 13 oct 2017

    Roscoff, du 9 octobre au 13 octobre

    Comité d'organisation : Paul Baird, Gilles Carron, Ali Fardoun, Carl Tipler

    Comité scientifique : Gérard Besson (CNRS, Institut Fourier), Olivier Biquard (ENS Paris), Ahmad El Soufi (Univ. Tours)

    L'analyse géométrique est une discipline à l'interface entre l'analyse des équations aux dérivées partielles et de la géométrie riemannienne ; c'est également un outil fondamental en physique mathématique. Cette thématique a connu des développements spectaculaires ces dernières d'années : résolution des conjectures de Poincaré, de Willmore, de Lawson, de Yau-Tian-Donaldson. Ces avancées ont également permis d'élargir la palette des outils utilisés (théorie géométrique de la mesure, définition de la courbure de Ricci pour des espaces métriques, transport optimal...). Cette conférence sera l'occasion de faire rencontrer des spécialistes de différents domaines pour confronter les questions des différents sujets et les outils utilisés.

  • Conférence - Rencontres doctorales Lebesgue 2017
    16 oct 2017 - 18 oct 2017

    Rennes, du 16 octobre au 18 octobre

    Comité d'organisation : Grégory Boil, Valentin Doli, Caroline Robet, Jérôme Spielmann

    Comité scientifique : Solène Bulteau, Clément Rouffort, Nasab Yassine

    Depuis trois ans, le Centre Henri Lebesgue soutient les Rencontres doctorales Lebesgue, initiative des doctorants du Labex. Il s'agit de trois journées de conférences durant lesquelles la parole est donnée à des doctorants de tout horizon géographique et mathématique. L'objectif est ainsi de présenter un panel le plus large possible de la recherche mathématique actuelle telle qu'elle est vue et vécue par les doctorants, mais pas seulement... Lors de ces rencontres, trois chercheurs, appelés 'parrains' de l'évènement, sont invités à exposer et ainsi à partager leur expérience personnelle de la recherche d'aujourd'hui. Cette année, les rencontres sont parrainées par :

    Jean-Marc Bardet (SAMM, Université Paris 1);

    Jasmin Raissy (Institut mathématique de Toulouse, Université Paul Sabatier);

    Gabriel Rivière (Laboratoire Paul Painlevé, Université Lille 1).

    Bien que principalement destinée aux doctorants, cette conférence se veut également accessible aux étudiants de M2 désireux d’avoir un aperçu des travaux auxquels une thèse en mathématiques peut mener. Pour les doctorants désireux d'exposer leurs travaux de recherche, il est également possible de déposer une proposition sur l'onglet 'Proposer un Exposé'. Dans un souci d'organisation, merci de vous inscrire à l'évènement même si vous proposez un exposé.

  • XVII Journées Louis Antoine
    19 oct 2017 - 20 oct 2017

    Nombres et aléas

    Deux mini-cours de 3 heures

    Yann Bugeaud (Strasbourg): Sur l'écriture d'un nombre réel dans des bases différentes.

    et

    Ashkan Nikeghbali (Zürich):L'heuristique matrices aléatoires en théorie des nombres.

    et un exposé complémentaire

    Joackim Bernier (Université de Rennes 1) : Markoff, et approximation diophantienne.

    Voir le site des JLA

  • Complex dynamics and quasi-conformal geometry
    23 oct 2017 - 25 oct 2017

    Our colleague Tan Lei passed away in April 2016. A conference will be held from 23/10/2017 to 25/10/2017 at the University of Angers to honour her memory.

    Scientific Committee

    Etienne Ghys (ENS Lyon)
    John Milnor (Stony Brook)
    Mitsuhiro Shishikura (Kyoto).

    Organizing Committee

    Mohammed El Amrani (Angers)
    Michel Granger(Angers)
    Jean-Jacques Loeb(Angers)
    Laurent Meersseman(Angers)
    Pascale Roesch(Toulouse).

    Provisional list of speakers

    Xavier Buff, Arnaud Cheritat, Nuria Fagella (to be confirmed), Cui Guizhen,Peter Haissinski, John Hamal Hubbard (to be confirmed), Carsten lunde Petersen, Kevin Pilgrim, Mary Rees, Pascale Roesh, Hans Henrik Rugh, Dylan Thurston, Mitsu Shishikura, Giulio Tiozzo.

    More information : page

    The registration process is already open.

  • École - Masterclass 2017
    19 déc 2017 - 21 déc 2017

    QR-Code

    Angers, du 19 décembre au 21 décembre

    Comité d'organisation : Etienne Mann

    La Masterclass se déroulera à Angers du 19 au 21 décembre. Le matin, il y aura les cours. On aura deux sessions en parallèle.

    • Etienne Mann : Introduction aux champs algebriques.
      On définira les notions de catégories fibrés, topologies de Grothendieck et de champs.
    • Loic Chaumont: Application du théorème de Kirchhoff "matrix-tree-theorem"

    L'organisation payera l'hébergement et le repas de midi. Les autres repas seront à la charge des participants. Pour le transport, on fera le maximum dans la limite de notre budget.

    Deadline for registration 15 november

  • Workshop - Méthodes numériques pour les courbes algébriques
    19 fév 2018 - 23 fév 2018

    QR-Code

    Rennes, du 19 février au 23 février

    Comité d'organisation : Xavier Caruso, David Lubicz, Christophe Ritzenthaler, Marie-Françoise Roy

    Comité scientifique : Xavier Caruso, David Lubicz, Christophe Ritzenthaler, Marie-Françoise Roy

    Cette conférence sera l'occasion de réunir des chercheurs en géométrie algébrique complexe ou réelle et en mathématiques appliquées (à la physique ou à la cryptographie) pour échanger autour des méthodes numériques et des problèmes ouverts pour les courbes algébriques. Chaque thématique sera introduite par un exposé et suivie par des exposés de recherche. Les thématiques retenues sont les suivantes - Physique théorique/EDP - Calcul avec la jacobienne  - Topologie aléatoire réelle - Complexité du calcul de la topologie des courbes algébriques réelles - Méthodes p-adiques et application à la cryptographie

  • Conférence - Journées Maths et entreprise
    12 avr 2018 - 13 avr 2018

    QR-Code

    Vannes, du 12 avril au 13 avril

    Comité d'organisation : Christophe Berthon, Eric Darrigrand, Emmanuel Frénod, Fabrice Mahé, Loïc Chaumont

Conférence - Familles de Systèmes Dynamiques Algébriques

Rennes, du 12 juin au 16 juin

Comité d'organisation : Serge Cantat, Christophe Dupont

Comité scientifique : Matthew Baker, Eric Bedford, Serge Cantat, Christophe Dupont, Mattias Jonsson

Mini-courses :

  • Bertrand Deroin (Ecole Normale Supérieure, Paris) Holomorphic families of representations in SL(2,C)

We will survey some aspect of the theory of holomorphic families representations in SL(2,C):
1. Sullivan's stability theory
2. Bifurcation currents
3. Harmonic measures of complex projective structures

  • Charles Favre (Ecole Polytechnique, Palaiseau) Degeneration of rational maps of the Riemann sphere

We shall describe how one can control the dynamics of a meromorphic family of rational maps of the Riemann sphere parameterized by the punctured unit disk as one approaches the puncture. Our analysis is based in a crucial way on the interplay between complex and non-archimedean dynamics. We shall also review how this control can be combined with technics from arithmetic geometry to the description of the special curves in the parameter space that contain infinitely many post-critically finite maps.

  • Laura de Marco (Northwestern University, Chicago) Rational maps, elliptic curves, and heights

We will study the geometry and arithmetic of families of rational maps and families of elliptic curves. The focus will be on "canonical height functions", introduced by Tate and Neron around 1960 in the setting of abelian varieties and further developed by Call and Silverman (1993) for algebraic dynamical systems. My aim is to present recent results -- both in the setting of elliptic curves and of rational maps -- and to present open questions inspired by the connections between holomorphic dynamics and arithmetic geometry.

Talks :

  • François Berteloot (Toulouse): Bifurcations within holomorphic families of endomorphisms of P^k
  • Simon Brandhorst (Hannover): On the dynamical spectrum of projective K3 surfaces
  • Romain Dujardin (Université Paris 6): Degenerations of SL(2,C) representations and Lyapunov exponents
  • Alexander Gamburd (City University of New-York): Markov triples and strong approximation
  • Thomas Gauthier (Université de Picardie Jules Verne, Amiens): The support of the bifurcation measure has positive volume
  • Martin Hils (Paris): Model theory of compact complex manifolds with an automorphism
  • Sarah Koch (Ann Harbor): Irreducibility of curves in parameter space: cubic polynomials vs. quadratic rational maps
  • Holly Krieger (Cambridge University): Reduction of dynatomic curves
  • Juan Rivera-Letelier (Rochester): Hecke and Linnik
  • Thomas Scanlon (Berkeley University): Applications of characterizations of skew-invariant varieties
  • Tom Tucker (Rochester): Towards a finite index conjecture for iterated Galois groups
  • Junyi Xie (Université de Rennes 1): Invariant pencils for polynomial selfmaps of the affine plane

Abstracts :

François Berteloot : Bifurcations within holomorphic families of endomorphisms of P^k.

Simon Brandhorst : On the dynamical spectrum of projective K3 surfaces.

The dynamical degree of a surface automorphism is a Salem number, that is, an algebraic integer lambda>1 which is conjugate to 1/\lamda and all whose other conjugates lie on the unit circle. We prove that for each Salem number lambda of degree at most 20, there is a power lambda^n, n in N, which is the dynamical degree of an automorphism of some projective K3 surface.

Romain Dujardin : Degenerations of SL(2,C) representations and Lyapunov exponents

The talk is a report of work in progress with Bertrand Deroin and Charles Favre. Let G be a finitely generated group endowed with some probability measure mu and (rho_lambda) be an algebraic family of representations of G into SL(2,C), diverging in the representation space as lambda converges to infinity. Using non-Archimedean techniques, we study the asymptotics of the random product of matrices induced by rho_lambda(G,mu) as lambda converges to infinity. In particular we can describe the growth rate of the Lyapunov exponent in terms of non-Archimedean data.

Alexander Gamburd : Markov triples and strong approximation.

Thomas Gauthier : The support of the bifurcation measure has positive volume.

The moduli space M_d of degree d>=2 rational maps can naturally be endowed with a measure mu_bif detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation measure mu_bif has positive Lebesgue measure. To do so, we establish a general criterion for the conjugacy class of a rational map to belong to the support of mu_bif and we exhibit a "large" set of Collet-Eckmann rational maps which satisfy that criterion. As a consequence, we get a set of Collet-Eckmann rational maps of positive Lebesgue measure which are approximated by hyperbolic rational maps. This is a joint work with Matthieu Astorg, Nicolae Mihalache and Gabriel Vigny.

Martin Hils : Model theory of compact complex manifolds with an automorphism

One may develop the model theory of compact complex manifolds (CCM) with a generic automorphism in rather close analogy to what has been done for existentially closed difference fields, in important work by Chatzidakis and Hrushovski, among others. The corresponding first order theory CCMA provides a model-theoretic framework for the study of meromorphic dynamical systems. In the talk, I will present some results from 'geometric model theory' which hold in CCMA (e.g. the Zilber trichotomy for 'finite-dimensional' types). This is joint work with Martin Bays and Rahim Moosa.

Sarah Koch : Irreducibility of curves in parameter space: cubic polynomials vs. quadratic rational maps

Living inside the space of monic centered cubic polynomials, are the curves S_n, which consist of all polynomials f which possess a superattracting cycle of period n. Recently, Arfeux and Kiwi announced a proof that S_n is irreducible for all n>=1. In this talk, we consider the analogous curves which live in the moduli space of quadratic rational maps. It is currently unknown if these curves are irreducible. We discuss some unexpected challenges that arise in the quadratic rational map setting which are absent in the cubic polynomial setting. This talk is based on joint work with E. Hironaka.

Holly Krieger : Reduction of dynatomic curves

Dynatomic curves parametrize n-periodic orbits of a one-parameter family of polynomial dynamical systems. These curves lack the structure of their arithmetic-geometric analogues (modular curves of level n) but can be studied dynamically. Morton and Silverman conjectured a dynamical analogue of the uniform boundedness conjecture (theorems of Mazur, Merel), asserting uniform bounds for the number of rational periodic points for such a family. I will discuss recent work towards the function field version of their conjecture, including results on the reduction mod p of dynatomic curves for the quadratic polynomial family z^2+c.

Juan Rivera-Letelier (Rochester): Hecke and Linnik

I will discuss the equidistribution of Hecke operators of p-adic elliptic curves. The most difficult case, of supersingular elliptic curves, is analyzed using Lubin-Katz theory of the canonical subgroups, and the period map of Serre-Tate's theory on the deformation of fomal groups. The key ingredient is a version of Linnik's equidistribution theorem for a certain p-adic quaternion algebra. This is a joint work with Sebastian Herrero and Ricardo Menares.

Thomas Scanlon : Applications of characterizations of skew-invariant varieties

In work with Medvedev, I classified the skew-invariant subvarieties of so-called split polynomial dynamical systems. Here, a split polynomial dynamical system is one of the form F: A^n to A^n given in coordinates as (x_1,...,x_n) -> (f_1(x_1), f_2(x_2),..., f_n(x_n)) where each f_i is a polynomial in one variable. The "skew" in "skew-invariant" means that we work over a field K equipped with an endomorphism sigma : K -> K. A subvariety V of A^n is skew-invariant if F maps V to V^sigma, the transform of V under sigma. In most applications of our theorem to date, only the case that sigma is the identity is used and the resulting classification of the invariant varieties may be obtained from methods of complex dynamics, as shown by Pakovich. In this lecture, I will speak about two applications which make essential use of the generalization to skew-invariance: a theorem proven jointly with Medvedev and Nguyen that Mahler functions of polynomial type with respect to multiplicatively independent exponents are algebraically independent and a project with Medvedev to extend our classification of (skew-)invariant varieties to what we call triangular dynamical systems (though what have been called skew-products in the literature): algebraic dynamical systems of the form F : A^n to A^n given in coordinates as (x_1,...,x_n) -> (f_1(x_1),f_2(x_1,x_2),...,f_n(x_1,...,x_n)) where f_i is a polynomial in the variables x_1,..., x_i.

Tom Tucker : Towards a finite index conjecture for iterated Galois groups

Let f be a polynomial over a global field. Let G denote the inverse limits of the Galois groups of f^n, where f^n denotes n-th iterate of f. Boston and Jones have suggested that under reasonable hypotheses, one might hope that G has finite index in the full group of automorphisms on an infinite tree corresponding to roots of iterates f^n when f is quadratic. We will show that their conjecture is true over function fields of characteristic 0, and that it would be a consequence of well-known diophantine conjectures over number fields. We will also treat the case of cubic polynomials, where less is known.

Junyi Xie : Invariant pencils for polynomial selfmaps of the affine plane

With Jonsson and Wulcan, we classify polynomial selfmaps f of the affine plane of that preserve an irreducible pencil of curves at infinity. More generally, we study a more general classification problem, where the invariant pencil is replaced by more general numerical data at infinity.

Partenaires

Irmar LMJL ENS Rennes LMBA LAREMA

Tutelles

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENSRennes UBO UBS Angers UBL