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  • Conference - Lebesgue PhD meeting 2016
    Oct 19, 2016 to Oct 21, 2016

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    Angers, from October 19th to October 21st

    Organization board: Clément du Crest de Villeneuve, Clément Fromenteau, Guillaume Roux, Johan Leray

    Scientific board: Viet Anh Nguyen, Olivier Thom, Caroline Vernier

  • Conference - CAST - Contact and Symplectic Topology
    Jan 26, 2017 to Jan 28, 2017

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    Nantes, from January 26th to January 28th

    Organization board: Baptiste Chantraine, Vincent Colin, Paolo Ghiggini

    Scientific board: Jean-François Barraud, Baptiste Chantraine, Kai Cieliebak, Tobias Ekholm

  • School - Flows and Limits in Kähler Geometry
    Apr 18, 2017 to Apr 22, 2017

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    Nantes, from April 18th to April 22nd

    Organization board: Sébastien Boucksom, Yann Rollin, Carl Tipler

    Scientific board: Claudio Arezzo, Olivier Biquard, Paul Gauduchon, Michael Singer

    Kähler geometry is a very active research field, at the crossroads between algebraic and Riemannian geometry. Important breakthrough, that lead to solve the Yau-Tian-Donaldson conjecture in the Fano case, have been achieved recently. A spring school involving mini-lectures and talks around this thread of new ideas in Kähler geometry is organized at Nantes University. The goal of the school is to develop certain technical skills, useful to address a variety of important questions in algebraic geometry and global analysis on manifolds, aimed for PhD students and young researchers. Geometric flows, like the Kähler-Ricci flow for instance, and the associated quantification by the Donaldson dynamical system, will be among the essential tools dealt with during the school.

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

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    Angers, from April 24th to April 28th

    Organization board: Frédéric Mangolte, Etienne Mann, Laurent Meersseman

    Teichmüller theory and mirror symmetry are very active domains. In this conference, we propose two series of lectures by two world leaders :

    • Misha Verbitsky on Teichmüller theory
    • Hirochi Iritani on mirror symmetry

    Both will gave each morning an one hour lecture followed in the afternoon by more advanced results by internationnal mathematicians. The goal of this conference is to bring together matematicians from different backgrounds and also to give an overview of the subjetcs to young PhD and post-doc students.

    Lecturers:

    • Hiroshi Iritani, Kyoto University
    • Misha Verbitsky, HSE Moscow

    Speakers:

    • Gaetan Borot, Max Planck Institut, Bonn
    • Fabrizio Catanese, University of Bayreuth
    • Amerik Ekaterina, University of Orsay (tbc)
    • Maxim Kontsevich, IHES (tbc)
    • Thomas Reichelt, University of Heidelberg
    • Claude Sabbah, Ecole polytechnique
    • Andrei Teleman, University of Aix-Marseille
    • Dimitri Zvonkine, University Pierre et Marie Curie
  • Conference - Infinite measure Dynamics
    Jun 6, 2017 to Jun 9, 2017

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    Brest, from June 6th to June 9th

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

    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 - Dynamics of algebraic transformations
    Jun 12, 2017 to Jun 16, 2017

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    Rennes, from June 12th to June 16th

    Organization board: Serge Cantat, Christophe Dupont

  • Conference - Random walks on algebraic structures
    Jun 19, 2017 to Jun 23, 2017

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    Rennes, from June 19th to June 23rd

    Organization board: Bachir Bekka, Nizar Demni

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

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    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.

Conference - Loop spaces in geometry and topology

Nantes, from Sept 1st to 5th, 2014
Contact: H. Abbaspour
Organisation board: H. Abbaspour (Nantes), A. Oancea (Paris), N. Wahl (Copenhagen)

One-dimensional objects have played a central role in geometry for a long time. From lines in Euclidean spaces to geodesics in Riemannian manifolds, particular classes of real one-dimensional sub-objects of a given space, i.e. loops or paths, have been successfully used as probes for the ambient geometry. At the local level, Riemannian curvature can be classically recovered from the behavior of geodesic paths via the Jacobi equation. At the global level, landmark results such as Morse's development of the calculus of variations in the large (1929), Berger's classification of holonomy groups (1953), Gromoll and Meyer's homological criterion for the existence of infinitely many closed geodesics (1969), or its reinterpretation by Sullivan-Vigué from the viewpoint of rational homotopy theory (1976), have shown deep connections between spaces of loops and analysis, Lie group theory, or topology. From a quite different perspective, string theory considers loops and paths (strings), as well as Riemann surfaces (worldsheets), as the basic building blocks for a unified theory of matter.

On the mathematical side, symplectic geometry appears to be the most natural setup within which real 1-dimensional objects (loops/paths) interact with complex 1-dimensional objects (Riemann surfaces). Gromov's theory of pseudo-holomorphic curves (1985) and its reinterpretation by Floer as a variational theory for the unregularized gradient flow of the symplectic action functional (1987) proved to be a successful tool in order to address the Arnold and Weinstein conjectures (1986, 1979) on the existence of closed orbits/chords for Hamiltonian systems. The geometric structure of compactified moduli space of pseudo-holomorphic curves gives rise to sophisticated algebraic structures, and in particular to various homology theories such as Floer homology, (embedded) contact homology, Seiberg-Witten-Floer homology, ... In all of these theories, one introduces higher products that account for all the non-canonical choices that one needs to make in order to lift an associative product from homology to the chain level. These operations get organized into a differential which is a coderivation on a larger object known to algebraic topologists as the “Bar construction”.

Almost simultaneously and inspired by the algebraic structures encountered in quantum field theory, algebraic topologists have been trying to understand the chain complexes of free loop and path spaces of a manifold. Chas and Sullivan's natural idea of cutting and pasting loops/paths together with considering Poincaré duality for the underlying manifold has led to a plethora of operations and opened a new field known as “string topology”. In parallel to this topological approach, a lot of effort was put into understanding the algebraic structure of “algebraic loop spaces”, modeled as Hochschild complexes of DGAs or categories equipped with further structures that account for Poincaré duality in the topological setting.

The various procedures for assigning a linear object (complex, homology, category...) to a nonlinear object gave rise to rich homotopical structures. There are many striking (algebraic) similarities between the constructions and difficulties encountered in each of the previous three settings. The common desire to reorganize non-canonical choices into higher homotopies and categories has also led to more elegant formulations of geometric and topological statements in terms of derived categories and functors.

We think that the time is ripe to bring together experts and young mathematicians working in these areas. We expect fruitful interactions and hope to harvest inspiration and new ideas. To this end, we intend to have 5 mini-courses accessible to non-experts, followed by a few talks dealing with more recent developments.

Partners

Affiliation

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENS Cachan UBL