Séminaire Géométrie, analyse et dynamique

Séminaire Géométrie, analyse et dynamique


Laboratoire Dieudonné-CNRS-UNS UMR 7351

Le Séminaire a lieu le Mardi à 14h00 en salle I du LJAD

Accès au laboratoire J.A. Dieudonné

Prochain exposé

Mardi 20 Novembre            
     Gérard Iooss (LJAD)

Existence de quasipatterns dans la superposition de deux patterns hexagonaux

Let us consider a quasilattice, spanned by the superposition of two hexagonal lattices in the plane, differing by a rotation of angle ß. We study bifurcating quasipatterns solutions of the Swift-Hohenberg PDE, built on such a quasilattice, invariant under rotations of angle π /3. For nearly all ß, we prove that in addition to the classical hexagonal patterns, there exist two branches of bifurcating quasipatterns, with equal amplitudes on each basic lattice.

Au programme


Mardi 27 Novembre            
     Bram Petri (Uni Bonn)
Short geodesics on random hyperbolic surfaces

Random Surfaces can be used to study the geometric properties of typical (hyperbolic) surfaces of large genus. Moreover, they can sometimes be used in existence proofs. That is, sometimes the easiest way of proving that surfaces with certain properties exist is to prove that the probability that a random surface has these properties is non-zero. Of course there are multiple possible models of random surfaces. In this talk, a random surface will be a surface that is picked at random using the Weil-Petersson volume form on the moduli space of hyperbolic surfaces of a given genus. I will speak about the length spectrum of these random surfaces. This is joint work with Maryam Mirzakhani.


Mardi 4 Décembre            
     Raphaël Krikorian (Université de Cergy-Pontoise)
Sur la divergence des formes normales de Birkhoff

Mardi 11 Décembre            
     Yann Brenier

Mardi 18 Décembre            
     Journée de dynamique complexe
toute la journée du 18 décembre


Mardi 8 Janvier            
     Winter school on geometric structures
7-11 janvier

Mardi 29 Janvier            
     Journée GAD 2019

Orateurs/programme :

Thomas Waters 10h30

Samuel Tapie 11h40

Anders Karlsson 14h30

Sébastien Gouezel 15h40


Mardi 5 Février            
     Vincent Humilière (IMJ)

Mardi 26 Février            
     Alejandro Kocsard (UFF)


Mardi 26 Mars            
     Rémi Coulon

Exposés passés


Mardi 11 Septembre      Jayadev Athreya
Random Tesselations of Hyperbolic Surfaces

In joint work with Lalley, Sapir, and Wroten, we study the statistics of the tesselations of hyperbolic surfaces induced by long random geodesics. We show that the local statistics approach that of a Poisson Line Process. All relevant notions will be defined.

Mardi 25 Septembre      Xiang Zhang (Shanghai Jiao Tong University -- China)
Global and local integrability of differential systems and its application

In this talk we report the progress on the study of both global integrability and local integrability of ordinary differential systems, and also their applications. On global integrability we emphasis on algebraic aspects, especially Darboux theory of integrability and its relation with Liouvillian integrability. On local integrability, we concern the necessary and sufficient conditons of ordinary differential system in a neighborhood of a singular point, which has also connection with global integrability.


Mardi 2 Octobre      Qun Wang (CEREMADE, Université Paris-Dauphine)
Periodic Solution for Positive N-vortex Problem: Existence, Multiplicity and Symmetry.

The vortex dynamics finds its root in hydrodynamics with 160 years of history. In 1858 Hermann von Helmholtz’s seminal paper has marked its birth and then Kirchhoff in 1876 has shown its Hamiltonian structure. It is well known that for N>3 this problem is in general non-integrable, thus the searching of periodic solution serves as an important approach to understand the dynamics. Many interesting results in this fields are produced through methods developed in celestial mechanics, especially perturbative aspects. On the other hand, in recent years following the figure eight solution of Chenciner and Montgomery, variational methods have been proved to be very efficient in searching for periodic solutions in N-body problem. In this talk I would like to explore the possibility in application of classical variational methods in Hamiltonian system to the study of periodic solutions for N-vortex systems with positive vorticities in the plane, including their existence, multiplicity, and possible symmetry.

Mardi 9 Octobre      Alain Chenciner (ASD & Paris 7)
Les coordonnées actions-angles - Une simple histoire d’action de tore (d’après Nguyen Tien Zung)

On sait bien que l’existence de coordonnées actions-angles est intimement liée à l’action de tore associée à un système intégrable. Nguyen Tien Zung renverse le point de vue en montrant que tout tenseur préservé par le système l’est aussi par cette action. D’où tout s’ensuit.

Mardi 16 Octobre      Mauricio Poletti (Université Paris-Sud)
Positive exponents for random product of diffeomorphisms

We prove that in the space of C^r random product of volume preserving diffeomorphisms there exists a C^1 dense and C^1 open set with positive Lyapunov exponents. We actually prove this in the more general setting of skew products with a hyperbolic homeomorphism as a base map and for volume preserving skew products. This is a joint work with Davi Obata.


Mardi 6 Novembre      Indira Chatterji (LJAD)
Property (T) and relative property (T)

Introduced by David Kazhdan (1967) property (T) means that if a group G acts unitarily on a Hilbert space and has "almost invariant vectors", then it has a nonzero invariant vector. The relative version only asks for a nonzero vector invariant under a subgroup, and is an obstruction to the Haagerup property, which ensures a proper isometric action on an affine Hilbert space and has several important consequences. In this talk I will recall these notions and explain how relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself.

Mardi 13 Novembre      Peter Smillie (IHES)
Hyperbolic surfaces in Minkowski 3-space

I’ll present a characterization of all hyperbolic surfaces properly isometrically embedded in Minkowski 3-space. I'll then discuss possible applications of this characterization to the case where the hyperbolic surface is invariant under a discrete subgroup of isometrics of Minkowski space. This is joint work with Francesco Bonsante and Andrea Seppi.

Archives du séminaire de géométrie, analyse et dynamique: 2016/2017, 2017/2018
Archives du séminaire de géométrie et analyse: 2007/2008, 2008/2009, 2009/2010, 2010/2011, 2011/2012, 2012/2013, 2013/2014, 2014/2015, 2015/2016
Archives du séminaire de géométrie et dynamique: ici

Organisation: Zhiyan Zhao (écrire) et Emmanuel Militon (écrire)