Menu

• Informations
  • Présentation
  • Venir à l’Institut Fourier
  • Guide Invité
  • Conseil du Laboratoire
• Actualités
• Annuaire
  • Annuaire par thème ou fonction
  • Rechercher une personne
• Thèmes de recherche
  • Algèbre et géométries
  • Analyse
  • Combinatoire et didactique
  • Géométrie différentielle
  • Physique mathématique
  • Probabilités
  • Théorie des nombres
  • Topologie
• Activités scientifiques
  • Présentation
  • Journées et colloques
    • Archives
  • École d’été
    • Informations pratiques
    • Formulaire d’inscription
    • Archives des écoles d’été
    • 2012
    • 2011
    • 2010
    • 2009
    • 2008
    • 2007
    • 2006
  • Prépublications
    • Rechercher une publication
  • Thèses et HDR
    • Archives des thèses et habilitations
  • Actes TSG
  • Fête de la science
    • Liste des exposés
• Séminaires
  • Liste des séminaires
    • Rechercher un séminaire
    • Semainier
  • Groupes de travail
    • Rechercher un exposé
  • Colloque
  • Tripode
  • S’abonner à une liste de diffusion
• Relations internationales
  • Coopérations nationales
  • Coopérations internationales
  • Guid’Europe
  • Invités

• Formation
  • Site de l'U.F.R
  • École doctorale

• Webmail

Rechercher

Registration procedure :

Download the registration form and send it duly completed to geraldine.rahal@ujf-grenoble.fr

Getting to the Institut Fourier

List of hotels

Lyon Saint Exupéry shuttles

Schedule

Titles and abstracts

Laurent Bessières

Ricci flow with surgery on open -manifolds with bounded geometry

We develop a variant of Perelman’s Ricci flow with surgery, on -dimensional complete manifolds with bounded geometry. As an application, we classify such manifolds with scalar curvature  : each one is a connected sum (infinite) of copies of a finite number of spherical manifolds and . (Joint work with S. Maillot and G. Besson).

I shall present some new local results on Einstein metrics : unique continuation (an Einstein metric is completely determined by its first and second fundamental forms on an hypersurface) ; and a regularity result : polyhomogeneity at infinity (existence of an asymptotic expansion).

We will present different results and idea about harmonic function with L2 gradient, harmonic 1 forms, and the number of endsof complete Riemannian manifold. We will present different rigidity result about minimal hypersurface and hyperbolic manifold (results of P. Li & J. Wang and G. Besson & G. Courtois & S. Gallot).

In this talk we will discuss how the Ricci flow with surgery can be used to prove that the space of positive scalar curvature metrics on the three-sphere is path-connected. The proof also uses the connected sum construction of Gromov and Lawson together with the conformal method. The work of Perelman on Hamilton’s Ricci flow is fundamental. We will also discuss applications to the vacuum constraint equations of general relativity.

The main motivation comes from the method of passive imaging in seismology, developped by Michel Campillo and his group (LGIT, Grenoble). The potential in the Schrödinger operator can be recovered, under some weak genericity assumptions, from the spectrum of modulo . The proof uses Abel’s integral transform and several semi-classical trace formulae. Details can be found in the papers arXiv:0802.1605 and arXiv:0802.1643.

On compare le volume de certaines variétés de dimension trois avec la complexité de leurs groupes fondamentaux (travail en commun avec L. Potyagailo).

We show that a bi-invariant metric on a compact connected Lie group is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric on there is a positive integer such that, within a neighborhood of in the class of left-invariant metrics of at most the same volume, is uniquely determined by the first distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where is simple, can be chosen to be two. (This is joint work with Dorothee Schueth and Craig Sutton.).

On a Riemann surface Selberg trace formula can be expressed through the expression of the Laplacian determinant and Selberg zeta function. The lecture will consider the determinant for the Dirichlet to Neuman map.

I will begin by summarizing some well known topological obstructions to admitting metrics with various curvature conditions. I will then specialize to the problem of prescribing curvature conditions for conformal metrics, and describe some results for closed manifolds and manifolds with boundary.

I will survey some classical results about the multiplicity of eigenvalues of the standard Laplacian on compact manifolds, and present new results and open questions about multiple eigenvalues of the Hodge Laplacian.

Suppose, on a given closed 2-manifold, we have a family of negatively curved metrics that satisfy the Ricci flow. Anthony Manning showed in 2004 that the topological entropy associated to the geodesic flow of a metric is decreasing as we move along the path. We extend this result to a magnetic setting, where the Ricci Yang-Mills flow is a more appropriate geometric evolution equation.

In this talk, I will explain how to characterise using ergodic theory actions of free groups on the affine 3-dimensional space whose linear part is a fuchsian group. (joint work with Goldman and Margulis)

I will discuss surfaces in the 3-dimensional homogeneous spaces , Berger spheres, Heisenberg space, -tilda, and . Here, and are the sphere and hyperbolic plane of curvature one and minus one respectively. I describe some examples and theorems depending on the mean, intrinsic or extrinsic curvature of the surface.

Asymptotically hyperbolic manifolds are a natural generalization of infinite volume hyperbolic manifolds and enjoy similar features. In this talk, I will present results for the Laplace and length spectra of dimension asymptotically hyperbolic manifolds with negative (but not necessarily constant) sectional curvatures. These results include : a dynamical wave trace formula relating the Laplace and length spectra, a prime orbit theorem for the geodesic flow based on the dynamical zeta function, and a relationship between the pure point spectrum of the Laplacian and the topological entropy of the geodesic flow. Key techniques and ideas from the proofs will be summarized, concluding with a discussion of open problems.

We present some results about the growth of quotients of a general Kleinian group (i.e. a discrete, torsionless group of isometries of a Cartan-Hadamard manifold with curvature pinched between two negative constants). Namely, we give general criteria ensuring the divergence of a quotient of and the "critical gap property" . As a corollary, we prove growth tightness of geometrically finite Kleinian groups satisfying the parabolic gap condition (this means that for every parabolic subgroup of ). Notice that, as these quotient groups naturally act on non-simply connected quotients of a Cartan-Hadamard manifold, the classical arguments of Patterson-Sullivan’s theory (topology of the boundary, shadows, quasi-conformal densities etc.) are not available here. This forces us to a more elementary approach for counting points in the orbit of a quotient (which gives a new elementary proof of the classical results of divergence of geometrically finite groups in the simply connected case). We also notice that, contrary to the simply connected case, there is large freedom for the behaviour of the growth function of quotients of Kleinian groups (even convex-cocompact) : as a way of example, we will exhibit quotients of convex cocompact Kleinian groups with mixed polynomial-exponential growth. (joint work with F.Dal’Bo, M.Peigne, J.C.Picaud)

We consider the integrals of -mean curvatures of a complete hypersurface in space forms which generalize volume , total mean curvature , total scalar curvature and total curvature . Among other results we prove that a complete properly immersed hypersurface of a space form with , and for some has This is a joint work with H. Alencar and D. Zhou.

The first half of the talk will be a brief survey of the geometry and topology of manifolds with positive isotropic curvature. The second half will deal with recent results about metric and smooth rigidity of Einstein metrics with positive isotropic curvature.

In the second volume of the Mathematische Annalen (1874), in which he determines the maximal domains of stability of the catenoid in R^ 3 .
We will introduce a geometric approach to extend Lindelöf results to certain geometric situations in several ambient spaces.
This is a joint work with Pierre Bérard (Institut Fourier, Grenoble).

Using the Bochner technique, Steve Kerckhoff and I recently proved the following theorem. Let be a compact hyperbolic manifold with totally geodesic boundary. If has dimension at least four, then the holonomy representation of is infinitesimally rigid. This is an infinite volume analog of the Calabi-Weil rigidity theorem. I will explain some of the background and ideas used in the proof.

I will discuss some theorems regarding sequences of anti-self-dual metrics limiting to orbifold metrics, and give various examples and connections with the orbifold Yamabe problem.

registration_SpectralThGeo - 23 ko

Schedule - 26.2 ko