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  • Conference - Teichmüller Theory in Higher Dimension and Mirror Symmetry
    Apr 24, 2017 to Apr 28, 2017

    Angers, from April 24th to April 28th

    Organization board: Frédéric Mangolte, Etienne Mann, Laurent Meersseman, Alexis Roquefeuil

    Teichmüller theory and mirror symmetry are very active domains. In this conference, we propose two series of 5 talks by two world leader mathematicians :

    • Misha Verbitsky, Teichmüller theory, National Research University Higher School of Economics
    • Dimitri Zvonkine, cohomological field theory, University Pierre et Marie Curie

    Speakers:

    • Gaetan Borot, Max Planck Institut, Bonn
    • Fabrizio Catanese, University of Bayreuth
    • Ekaterina Amerik, University of Orsay
    • Maxim Kontsevich, IHES (tbc)
    • Thomas Reichelt, University of Heidelberg
    • Jacopo Stoppa, SISSA
    • Claude Sabbah, Ecole polytechnique
    • Adrien Sauvaget, University Pierre et Marie Curie
    • Andrei Teleman, University of Aix-Marseille
  • 5 minutes Lebesgue
    Apr 28, 2017

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

    Prochain exposé :

    28-04-2017:  Niccolo Torri
    Le problème de numérotation des sièges dans le train

    Cette semaine nous ferons un peu de combinatoire autour d'un problème qui nous touche lors d'un grand voyage en train: imaginons que nous nous rendons tardivement à la gare, nous sommes les derniers à monter dans le train. Après la grande course pour arriver à prendre le train nous souhaitons trouver notre place libre... mais est-ce que quelqu'un l'a déjà prise? Dans ce "5 minutes Lebesgue" nous allons calculer la probabilité de trouver notre place libre (avec quelques hypothèses sur le comportement des voyageurs).

    Lieu

    Nantes

    Exposés à venir:

    09-05-2017:  Éric Darrigrand

  • Séminaire Quimpériodique
    Jun 1, 2017 to Jun 2, 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

    Inas Amacha (LMBA): TBA;
    Vincent Colin (LMJL): TBA;
    Bertrand Deroin (ENS Paris): TBA;
    Victor Kleptsyn (IRMAR): TBA;
    Paul Laurain (univ. Paris VII): TBA.

    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

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  • Conference - Infinite measure Dynamics
    Jun 6, 2017 to Jun 9, 2017

    Brest, from June 6th to June 9th

    Organization board: Yves Coudène, François Maucourant, Françoise Pène, Barbara Schapira, Samuel Tapie, Annick Nicolle

    Scientific board: Jon Aaronson, Jean-Pierre Conze, Gilles Courtois, Domokos Szasz

    This conference will focus on dynamical systems which naturally preserve a measure with infinite mass. These systems appear in a geometric or probabilistic context, or may come from natural sciences. When the invariant measure has infinite mass, recurrence is no longer automatic, usual mixing properties disappear and new asymptotical properties (such as rationnal ergodicity) may occur. Such systems may develop various and subtil behaviours, which could not exists in finite measure dynamics.

    This conference will gather international experts on this topic, and will allow young researcher to have an easy access to the large recent developpment on such questions.

  • Conference - Families of algebraic dynamical systems
    Jun 12, 2017 to Jun 16, 2017

    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)
    • Romain Dujardin (Université Paris 6)
    • Alexander Gamburd (City University of New-York)
    • Thomas Gauthier (Université de Picardie Jules Verne, Amiens)
    • Martin Hils (Paris)
    • Sarah Koch (Ann Harbor)
    • Holly Krieger (Cambridge University)
    • Juan Rivera-Letelier (Rochester)
    • Thomas Scanlon (Berkeley University)
    • Tom Tucker (Rochester)
    • Junyi Xie (Université de Rennes 1)
  • Conference - Random walks on algebraic structures-On honour of Yves Guivarc'h
    Jun 19, 2017 to Jun 23, 2017

    Rennes, from June 19th to June 23rd

    Organization board: Bachir Bekka, Nizar Demni

    Scientific board: Bachir Bekka, Emmanuel Breuillard, Nizar Demni, Alex Lubotzky

    The conference deals with themes around random walks on algebraic structures. Dynamical sytems on groups, homogeneous spaces, and related structures (graphs, quantum groups , groupoids,...) are rich objects, involving various fields of mathematics (probability, group theory, topology, number theory, operator algebras, Banach space geometry, etc). They are also useful as modelling tools for other sciences (physics, computer science, economics, etc); for instance, expander graphs, which are of interest in theoretical computer science, are graphs for which the associated random walk has special spectral properties and their explicit construction involves sophisticated tools such as Kazhdan's property (T) or Selberg's inequality. The conference aims to give a flavor of the various aspects of the subject by bringing together some experts with major contributions to the field. This conference will also be the opportunity to celebrate the 80th birthday of Yves Guivarc'h, who played a major part in the development of probability on algebraic and geometric structures, a subject with an ever growing interest for the last 30 years.

  • Conference - Dynamics on representation varieties
    Jun 26, 2017 to Jun 30, 2017

    Rennes, from June 26th to June 30th

    Organization board: Ian Biringer, Ludovic Marquis, Juan Souto

    Scientific board: Uri Bader, Jeffrey F. Brock, Jean-Marc Schlenker

    Numerous areas of mathematics are touched by what could be called Dynamics on representation varieties. For instance one could mention ergodic theory, Riemannian geometry, low-dimensional topology, Teichmüller theory, and so on... The aim of this workshop is to bring together graduate students, recent graduates and experts in these different areas, giving everybody ample time for discussions and collaborations. Next to a number of research talks, three mini-courses by Tsachik Gelander, Francois Labourie and Julien Marché will take place.







    We the organizers of this conference affirm that scientific events must be open to everyone, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We believe that such events must be supportive, inclusive, and safe environments for all participants. We believe that all participants are to be treated with dignity and respect. Discrimination and harassment cannot be tolerated. We are committed to ensuring that the Conference Dynamics on representation varieties follows these principles. For more information on the Statement of Inclusiveness, see this dedicated web page.

  • School - Analytical aspects of hyperbolic flows
    Jul 3, 2017 to Jul 7, 2017

    Nantes, from July 3rd to July 7th

    Organization board: Sebastien Gouëzel, Laurent Guillopé, Samuel Tapie

    Scientific board: Nalini Anantharaman, Viviane Baladi, Colin Guillarmou, Masato Tsujii

    Hyperbolic flows are dynamical systems with strong chaotic properties, whose study has been started a long time ago, a crucial example being the geodesic flow on negatively curved manifolds. Whereas the qualitative properties of such flows are well understood, their fine quantitative properties (rate of mixing, spectrum...) require more sophisticated tools. They have been studied both from a dynamical point of view (Dolgopyat's techniques) and more analytically: semi-classical methods, initially introduced to study PDEs, have proven very valuable in this context.

    The purpose of this summer school is to make these different techniques accessible to PhD students and young researchers, as well as to give an opportunity for specialists in dynamical systems to learn tools from semi-classical analysis, and conversely. Therefore, the core of this summer school will consist in three introductive mini-courses, completed by a few research talks and question sessions.

School - Flows and Limits in Kähler Geometry

List of (confirmed) speakers

Mini-courses :

Talks :

Titles and abstracts

  • Bo Berndtsson (Chalmers University) : Direct image bundles and variations of complex structures

Given a smooth proper fibration $p:\mathcal X\to B$ and $L$ a line bundle over $\mathcal X$, the direct image $$ E:= p_*(L) $$ is in many cases a holomorphic vector bundle over $B$. Its fibers are the spaces of holomorphic sections of $L$ over the fibers of $p$, $X_t=p^{-1}(t)$, and they can be given various $L^2$-metrics. In case the fibration is of relative dimension $n$ so that the fibers are compact Riemann surfaces, special cases of this situation can be used to study the variation of complex structures on the fibers $X_t$. (The fibers are all diffeomorphic, but their complex structure varies with $t$, so we can view the family $X_t$ as a family of variations of complex structures on one fixed smooth manifold.) When the relative dimension is higher than one the situation is more complicated and one needs to consider also higher direct images. I will discuss the problems that arise in this connection, with previous work of Siu, Schumacher and To-Yeung and some recent joint work with Xu Wang and Mihai Paun.

  • Hans-Joachim Hein (Fordham University) : Tangent cones of Calabi-Yau varieties

It has been known for about 10 years that the classical Calabi-Yau theorem on the existence and uniqueness of Ricci-flat Kahler metrics on smooth complex manifolds with zero first Chern class can be extended to a natural setting of weak Kahler metrics on singular complex varieties. However, until relatively recently nothing was known - even in the simplest nontrivial examples - about the precise asymptotic behavior of these weak Ricci-flat metrics at the singularities of the underlying varieties. I will explain work of Donaldson-Sun, H-Naber and H-Sun that resolves this question in certain cases.

  • Valentino Tosatti (Northwestern University) : Metric Limits of Calabi-Yau Manifolds

In this mini-course I will give an introduction to the study of limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. Analytically, the problem is to prove suitable uniform a priori estimates for solutions of a degenerating family complex Monge-Ampère equations, away from some singular set. Geometrically, this can be used to understand the Gromov-Hausdorff limit of these metrics. And if the manifold is projective algebraic and the limiting class is rational, the limits possess an algebraic structure and are obtained from the initial manifold via contraction morphisms from Mori theory.

  • Jeff Viaclovsky (Wisconsin University) : The geometry of SFK ALE metrics

I will discuss some of the basics of scalar-flat Kaehler (SFK) metrics, and focus on the geometry of SFK metrics which are asymptotically locally Euclidean (ALE). These space arise as "bubbles" in the compactness theory of Calabi's extremal Kaehler metrics. I will also present some of the deformation theory of SFK ALE metrics.

  • Thibaut Delcroix (ENS Paris) : Kähler geometry of horospherical manifolds

Horospherical manifolds form a class of almost homogeneous manifolds whose Kähler geometry is very close to that of toric manifolds. They strictly contain homogeneous toric bundles, to which a lot of results holding for toric manifolds have been extended. I will present horospherical manifolds, trying to convince you that they are not much harder to deal with, and in particular I will present the criterion for K-stability in the Fano case that follows either from my work on spherical varieties, or from a direct, Wang-Zhu type, approach.

  • Eleonora Di Nezza (Imperial College) : Monge-Ampère energy and weak geodesic rays

The recent proof of Demailly's conjecture by Witt Nyström gives another evidence that pluripotential theory play a key role when working with complex Monge-Ampère equations in order to solve problems in differential and algebraic geometry. In this talk we investigate pluripotential tools: we characterise Monge-Ampère energy classes in terms of envelopes. And in order to do that, we develop the theory of weak geodesic rays in a big cohomogy class. We also give a positive answer to an open problem in pluripotential theory. This is a joint work with Tamas Darvas and Chinh Lu.

  • Jakob Hultgren (Chalmers University) : Coupled Kähler-Einstein Metrics

A central theme in complex geometry is to study various types of canonical metrics, for example Kähler-Einstein metrics and cscK metrics. In this talk we will introduce the notion of coupled Kähler-Einstein (cKE) metrics which are k-tuples of Kähler metrics that satisfy certain coupled Kähler-Einstein equations. We will discuss existence and uniqueness properties and elaborate on related algebraic stability conditions. (Joint work with David Witt Nyström)

  • Zakarias Sjostrom Dyrefelt (Université de Toulouse) : K-stability of constant scalar curvature Kähler manifolds

In this talk we introduce a variational/pluripotential approach to the study of K-stability of Kähler manifolds with transcendental cohomology class, extending a classical picture for polarised manifolds. Our approach is based on establishing a formula for the asymptotic slope of the K-energy along certain geodesic rays, from which we deduce that cscK manifolds are K-semistable. Combined with a recent properness result of R. Berman, T. Darvas and C. Lu we further deduce uniform K-stability of cscK manifolds with discrete automorphism group, thus confirming one direction of the YTD conjecture in this setting. If time permits we also discuss possible extensions of these results to the case of compact Kähler manifolds admitting holomorphic vector fields.

Partners

Irmar LMJL ENS Rennes LMBA LAREMA

Affiliation

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