Publications

2008

• Rigidity of amalgamated product in negative curvature
  
  • Besson Gérard
  • Courtois Gilles
  • Gallot Sylvain
  Journal of Differential Geometry, International Press, 2008, 79 (3), pp.335-387. Let $\Gamma$ be the fundamental group of a compact n-dimensional riemannian manifold X of sectional curvature bounded above by -1. We suppose that $\Gamma$ is a free product of its subgroup A and B over the amalgamated subgroup C. We prove that the critical exponent $\delta(C)$ of C satisfies $\delta(C) \geq n-2$. The equality happens if and only if there exist an embedded compact hypersurface Y in X , totally geodesic, of constant sectional curvature -1, with fundamental group C and which separates X in two connected components whose fundamental groups are A and B. Similar results hold if $\Gamma$ is an HNN extension, or more generally if $\Gamma$ acts on a simplicial tree without fixed point.
• Non-selfadjoint perturbations of selfadjoint operators in two dimensions. IIIa. One branching point.
  
  • Sjostrand Johannes
  Canadian Journal of Mathematics. Journal Canadien de Mathématiques, 2008, pp.572-657.
• Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope.
  
  • Vergne Michèle
  , 2008, pp.15-33.
• Hamiltonian 2-forms in Kahler geometry IV: Weakly Bochner-flat Kahler manifolds
  
  • Apostolov Vestislav
  • Calderbank David M. J.
  • Gauduchon Paul
  • Tonnesen-Friedman C.
  Communications in Analysis and Geometry, International Press, 2008, 16 (1), pp.91-126.
• KAM for the non-linear Schrödinger equation - A short presentation
  
  • Eliasson Hakan
  • Kuksin Sergei
  , 2008, pp.361-376.
• Entropy and the localization of eigenfunctions
  
  • Anantharaman Nalini
  Annals of Mathematics, Princeton University, Department of Mathematics, 2008, 168 (2), pp.435-475. (10.4007/annals.2008.168.435)
  DOI : 10.4007/annals.2008.168.435
• Equivariant Chern characters with generalized coefficients
  
  • Paradan Paul-Emile
  • Vergne Michèle
  , 2008. These notes form the next episode in a series of articles dedicated to a detailed proof of a cohomological index formula for transversally elliptic pseudo-differential operators and applications. The first two chapters are already available as math.DG/0702575 and arXiv:0711.3898. In this episode, we construct the relative equivariant Chern character of a morphism of vector bundles, localized by a one form, and we prove a multiplicativity property of this generalized Chern character
• Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances.
  
  • Sjostrand Johannes
  Open Mathematics Journal, Bentham Open, 2008, pp.35-81.
• Classes d'homotopie de fractions rationnelles
  
  • Cazanave Christophe
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2008, 346 (3-4), pp.129-133. Soient k un corps de caractéristique différente de 2 et n⩾1 un entier ; on munit l'ensemble des classes d'homotopie " algébrique " de fractions rationnelles pointées de degré n à coefficients dans k d'une structure de monoïde gradué par n et l'on construit un isomorphisme entre ce monoïde et celui des orbites sous l'action de SLn(k) de formes bilinéaires symétriques non dégénérées sur kn, muni de la somme orthogonale. (10.1016/j.crma.2008.01.004)
  DOI : 10.1016/j.crma.2008.01.004
• The Abelian/Nonabelian Correspondence and Frobenius Manifolds
  
  • Ciocan-Fontanine Ionut
  • Kim Bumsig
  • Sabbah Claude
  Inventiones Mathematicae, Springer Verlag, 2008, pp.301-343. We propose an approach via Frobenius manifolds to the study (began in math.AG/0407254) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding ''abelianized'' quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds.
• Histoire d'un vecteur tricentenaire.
  
  • Guichardet Alain
  Gazette des Mathématiciens, Société Mathématique de France, 2008, 117, pp.23-33.
• Infinite Töplitz-Lipschitz matrices and operators
  
  • Eliasson Hakan
  • Kuksin Sergei
  Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées, Springer Verlag, 2008, 59 (1), pp.24-50. We introduce a class of infinite matrices (Ass′,s,s′∈Zd) , which are asymptotically (as |s| + |s′| → ∞) close to Hankel-Töplitz matrices. We prove that this class forms an algebra, and that flow-maps of nonautonomous linear equations with coefficients from the class also belong to it. (10.1007/s00033-006-6030-6)
  DOI : 10.1007/s00033-006-6030-6
• Suites de Sturm, indice de Maslov et périodicité de Bott
  
  • Barge Jean
  • Lannes Jean
  , 2008, pp.199. (10.1007/978-3-7643-8710-5)
  DOI : 10.1007/978-3-7643-8710-5
• Inverse zero-sum problems and algebraic invariants
  
  • Girard Benjamin
  Acta Arithmetica, Instytut Matematyczny PAN, 2008, 135 (3), pp.231-246. In this article, we study the maximal cross number of long zero-sumfree sequences in a finite Abelian group. Regarding this inverse-type problem, we formulate a general conjecture and prove, among other results, that this conjecture holds true for finite cyclic groups, finite Abelian p-groups and for finite Abelian groups of rank two. Also, the results obtained here enable us to improve, via the resolution of a linear integer program, a result of W. Gao and A. Geroldinger concerning the minimal number of elements with maximal order in a long zero-sumfree sequence of a finite Abelian group of rank two. (10.4064/aa135-3-3)
  DOI : 10.4064/aa135-3-3
• Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2
  
  • Sjostrand Johannes
  Annales Scientifiques de l'École Normale Supérieure, Gauthier-Villars ; Société mathématique de France, 2008, pp.511-571.
• Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances
  
  • Faure Frederic
  • Roy Nicolas
  • Sjöstrand Johannes
  Open math journal, 2008, 1, pp.35--81. In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable anisotropic Sobolev spaces and which govern the decay of dynamical correlations, can be treated as the quantum resonances of open quantum systems in the Aguilar-Baslev-Combes theory or the more recent Helffer-Sjostrand phase-space theory.
• Valuations and Plurisubharmonic Singularities
  
  • Boucksom Sébastien
  • Favre Charles
  • Jonsson Mattias
  Publications of the Research Institute for Mathematical Sciences, European Mathematical Society, 2008, 44 (2), pp.449-494. We extend to higher dimensions some of the valuative analysis of singularities of plurisubharmonic (psh) functions developed by the first two authors. Following Kontsevich and Soibelman we describe the geometry of the space V of all normalized valuations on C[x1,. .. , xn] centered at the origin. It is a union of simplices naturally endowed with an affine structure. Using relative positivity properties of divisors living on modifications of C n above the origin, we define formal psh functions on V, designed to be analogues of the usual psh functions. For bounded formal psh functions on V, we define a mixed Monge-Ampère operator which reflects the intersection theory of divisors above the origin of C n. This operator associates to any (n − 1)-tuple of formal psh functions a positive measure of finite mass on V. Next, we show that the collection of Lelong numbers of a given germ u of a psh function at all infinitely near points induces a formal psh functionûfunctionˆfunctionû on V. When ϕ is a psh Hölder weight in the sense of Demailly, the generalized Lelong number νϕ(u) equals the integral ofûofˆofû against the Monge-Ampère measure ofˆϕofˆ ofˆϕ. In particular, any generalized Lelong number is an average of valuations. We also show how to compute the multiplier ideal of u and the relative type of u with respect to ϕ in the sense of Rashkovskii, in terms ofûofˆofû andˆϕandˆ andˆϕ. (10.2977/prims/1210167334)
  DOI : 10.2977/prims/1210167334
• Quantum cohomology of the Grassmannian and alternate Thom-Sebastiani
  
  • Kim Bumsig
  • Sabbah Claude
  Compositio Mathematica, Foundation Compositio Mathematica / Cambridge University Press, Cambridge, 2008, pp.221-246. We introduce the notion of alternate product of Frobenius manifolds and we give, after [math.AG/0610265], an interpretation of the Frobenius manifold structure canonically attached to the quantum cohomology of G(r,n+1) in terms of alternate products. We also investigate the relationship with the alternate Thom-Sebastiani product of Laurent polynomials.
• On Distribution of Energy and Vorticity for Solutions of 2D Navier-Stokes Equation with Small Viscosity
  
  • Kuksin Sergei
  Communications in Mathematical Physics, Springer Verlag, 2008, 284 (2), pp.407-424. We study distributions of some functionals of space-periodic solutions for the randomly perturbed 2D Navier-Stokes equation, and of their limits when the viscosity goes to zero. The results obtained give explicit information on distribution of the velocity field of space-periodic turbulent 2D flows. (10.1007/s00220-008-0577-3)
  DOI : 10.1007/s00220-008-0577-3
• Espaces vectoriels de dimension finie et représentations de de Rham
  
  • Colmez Pierre
  Asterisque, Société Mathématique de France, 2008, 319, pp.117-186.
• Représentations triangulines de dimension 2
  
  • Colmez Pierre
  Asterisque, Société Mathématique de France, 2008, 319, pp.213-258.
• Sur le nombre d'éléments exceptionnels d'une base additive
  
  • Plagne Alain
  Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2008, 616, pp.47-65. In a paper recently published in Crelle's Journal, Deschamps and Grekos study asymptotically (when h tends to infinity) the quantity E(h), introduced by Erdős and Graham, and defined as the maximal number of elements which are necessary to the basicity of an additive basis of order h. They show that the maximal order of this function is (h/log h)^(1/2). The aim of this article is to show that the E function does not have oscillations but, to the contrary, does possess a regular asymptotic behaviour, that we determine explicitly. More precisely, we prove that E(h) ~ 2(h/log h)^(1/2).
• Tunnel effect for Kramers-Fokker-Planck type operators.
  
  • Sjostrand Johannes
  Annales Henri Poincaré, Springer Verlag, 2008, pp.209-274.
• Hommage à André Lichnerowicz (1915-1998)
  
  • Kosmann-Schwarzbach Yvette
  Gazette des Mathématiciens, Société Mathématique de France, 2008, 118, pp.52-56.
• Uniform independence in linear groups
  
  • Breuillard Emmanuel
  • Gelander Tsachik
  Inventiones Mathematicae, Springer Verlag, 2008, 173 (2), pp.225-263. We show that for any finitely generated group of matrices that is not virtually solvable, there is an integer m such that, given an arbitrary finite generating set for the group, one may find two elements a and b that are both products of at most m generators, such that a and b are free generators of a free subgroup. This uniformity result improves the original statement of the Tits alternative. (10.1007/s00222-007-0101-y)
  DOI : 10.1007/s00222-007-0101-y