Les vidéos des exposés seront mises en ligne quelques jours après l'exposé.
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).
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
Scientific board: Matthew Baker, Eric Bedford, Serge Cantat, Christophe Dupont, Mattias Jonsson
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.
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
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.
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.
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.
Perspectives in Analysis and Probability - Opening Conference
Dating back to Kolmogorov's construction of probabilistic diffusions from solutions of partial differential equations in the early 30's and the joint development of potential theory and Markov process in the early 50's, Analysis and Probability theory have never ceased their fruitful interactions, feeded by practical problems from physics, engineering, finance and others. The inaugural conference of the semester Perspectives in Analysis and Probability will provide a panorama of this domain of interaction, by gathering top international researchers at the interface of Analysis, Probability theory and Partial Differential Equations.