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  • Post-doc positions
    Oct 4, 2017 to Dec 1, 2017
    lebesgue_money.png Henri Lebesgue Center offers post-doc positions for researchers in mathematics.

    Description

    The Lebesgue Center and its partners, Région Bretagne & Région Pays de la Loire (DéfiMaths project), are opening applications for three post-doctoral positions in mathematics for a period of 2*12 months. The hired applicant will conduct his/her research at one of these Insitutes:

    Irmar of Rennes
    LMJL of Nantes
    LMBA of Brest and Vannes
    LAREMA of Angers

    The positions are open to all research areas present within the four Institutes. They do not include an obligation to teach.

    The net salary will be 2 100 Euros per month.

    Deadlines

    The application is open.

    Sending application: between the 4th of October 2017 and the 1st of December 2017.

    The positions are expected to begin on September 1st or October 1st, 2018.

    Eligibility

    Candidates must have completed a PhD in mathematics, or equivalent, at the date of taking office. The candidate must submit an original research project including a collaboration with one or more local researcher (s) of Irmar, LMJL,LMBA, or LAREMA.

    Applicants must complete the online form where they have to join the following documents:

    • CV describing the candidate's profile and professional experience (list of publications, research topics, activities)
    • Cover letter including the research project
    • At least two letters of recommendation, including one from the local researcher involved in the project

    For more information, please contact us at post-doctorant[at]lebesgue.fr.

    Selection

    The selection is carried by the Lebesgue Scientific Committee.

    Nominees

    2017-2018
    2016-2017
    2015-2016
    2014-2015
    2013-2014

  • Complex dynamics and quasi-conformal geometry
    Oct 23, 2017 to Oct 25, 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.

  • 5 minutes Lebesgue
    Oct 24, 2017

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

    Prochain exposé (rediffusion):

    24-10-2017:  Vincent Colin
    Comment mesurer la forme d'un espace ?

    Comment construire des espaces exotiques aux propriétés surprenantes et comment, par des expériences locales, en deviner la forme ? On se laissera guider par Henri Poincaré.

    Lieu

    Rennes

    Exposés à venir:

    07-11-2017:  Éric Hazane

    21-11-2017:  Marine Fontaine

    28-11-2017:  Roger Lewandowski

    05-12-2017:  Maria Cumplido

    19-12-2017:  Guy Casale

    06-02-2018:  Rozenn Texier-Picard

  • Séminaire Quimpériodique
    Nov 16, 2017 to Nov 17, 2017

    Ce séminaire de géométrie, complètement à l'Ouest, réunit à Quimper, trois fois l'an, pour deux journées, le jeudi et le vendredi, des géomètres venus des régions Bretagne et Pays de Loire.

    Programme

    Sorin Dumitrescu (Univ. Nice): Géométries de Cartan branchées
    Clément Fromenteau (LAREMA): Sur le champ de Teichmüller des surfaces de Hopf
    Ngoc-Phu Ha (LMBA Vannes): Invariants quantiques associés à la super-algèbre de Lie sl(2|1)
    Harold Rosenberg (IMPA): The geometry and topology of complete minimal surfaces and applications
    Caroline Vernier (LMJL): Théorèmes de recollement en géométrie Kählérienne

    Correspondants

    Guillaume Deschamps, LMBA, Brest
    Laurent Meersseman, LAREMA, Angers
    Gaël Meigniez, LMBA, Vannes
    Yann Rollin, LMJL, Nantes
    Frédéric Touzet, IRMAR, Rennes

    Historique

    Historique du séminaire

    Affiche

    Télécharger l'affiche ici

  • School - Masterclass 2017
    Dec 19, 2017 to Dec 21, 2017

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    Angers, from December 19th to December 21st

    Organization board: Etienne Mann

    We organize a masterclass in Angers, from 19th to 21st of December, 2017. Lectures will be in the morning sessions. We will have two parallel sessions:

    • Etienne Mann : Introduction to algebraic stacks
      We will introduce the notion of fibered category, Grothendieck topology and stacks. We will illustrate these notions on simple examples. These lectures are for Master (or PhD) students who had followed a introduction to algebraic geometry that is algebraic varieties and sheaves.
    • Loic Chaumont: Application of the matrix-tree-theorem

    The organisation board will pay the housing and the lunch. The other meals are not payed by the organizers. For the travel expenses, we will do our best in the limit of our budget.

    Date limite d'inscription 15 novembre.

  • Workshop - Numerical methods for algebraic curves
    Feb 19, 2018 to Feb 23, 2018

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    Rennes, from February 19th to February 23rd

    Organization board: Xavier Caruso, David Lubicz, Christophe Ritzenthaler, Marie-Françoise Roy

    This workshop will bring together researchers in complex and real algebraic geometry and applied mathematics (physics and cryptography) to discuss numerical methods and open problems on algebraic curves. There will be a number of introductory talks to each of the following topics and invited lectures from specialists: - Theoretical physics/DPE - Computations with the Jacobian - Random real topology - Complexity of computing topology of real algebraic curves - p-adic methods and applications to cryptography

  • Conference - Mathematics and Entreprises Days
    Apr 12, 2018 to Apr 13, 2018

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    Vannes, from April 12th to April 13th

    Organization board: Christophe Berthon, Eric Darrigrand, Emmanuel Frénod, Fabrice Mahé, Loïc Chaumont

  • School - Fundamentals and practice of finite elements
    Apr 16, 2018 to Apr 20, 2018

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    Roscoff, from April 16th to April 20th

    Organization board: Martin Costabel, Eric Darrigrand, Monique Dauge, Yvon Lafranche

    Scientific board: Monique Dauge (Univ. Rennes 1), Ilaria Perugia (TU Wien)

Conference - Families of algebraic dynamical systems

Rennes, from June 12th to June 16th

Organization board: Serge Cantat, Christophe Dupont

Scientific board: 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.

Partners

Irmar LMJL ENS Rennes LMBA LAREMA

Affiliation

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