Publications

2008

• 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.
• Bowling en solo : le déclin du capital social américain
  
  • Putnam Robert D.
  • Rey Olivier
  Conférence, Editions Conférence, 2008, 27, pp.417-440. Traduction de "Bowling Alone: America's Declining Social Capital" de Robert D. Putnam, paru dans Journal of Democracy, vol. 6, n°1, 1995, p. 65-78.
• Hamiltonian 2-forms in Kahler geometry, III: Extremal metrics and stability
  
  • Apostolov Vestislav
  • Calderbank David M. J.
  • Gauduchon Paul
  • Tonnesen-Friedman C.
  Inventiones Mathematicae, Springer Verlag, 2008, 173 (3), pp.547-601. (10.1007/s00222-008-0126-x)
  DOI : 10.1007/s00222-008-0126-x
• Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains
  
  • Golse François
  • Mahalov Alex
  • Nicolaenko Basil
  , 2008, pp.301-338. A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically resonant cylinders. Resonances of fast swirling Beltrami waves deplete the Euler nonlinearity. The resonant Euler equations are systems of three-dimensional rigid body equations, coupled or not. Some cases of these resonant systems have homoclinic cycles, and orbits in the vicinity of these homoclinic cycles lead to bursts of the Euler solution measured in Sobolev norms of order higher than that corresponding to the enstrophy.
• Tunnel effect for Kramers-Fokker-Planck type operators.
  
  • Sjostrand Johannes
  Annales Henri Poincaré, Springer Verlag, 2008, pp.209-274.
• Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
  
  • Kosmann-Schwarzbach Yvette
  Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2008, 4, pp.005. After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper. (10.3842/SIGMA.2008.005)
  DOI : 10.3842/SIGMA.2008.005
• 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
• Universal unfoldings of Laurent polynomials and tt* structures
  
  • Sabbah Claude
  , 2008, pp.1-29. This article surveys the relations between harmonic Higgs bundles and Saito structures which lead to tt* geometry on Frobenius manifolds. We give the main lines of the proof of the existence of a canonical tt* structure on the base space of the universal unfolding of convenient and nondegenerate Laurent polynomials.
• Fourier-Laplace transform of a variation of polarized complex Hodge structure, II
  
  • Sabbah Claude
  , 2008, pp.289-347. We show that the limit, by rescaling, of the 'new supersymmetric index' attached to the Fourier-Laplace transform of a polarized variation of Hodge structure on a punctured affine line is equal to the spectral polynomial attached to the same object. We also extend the definition by Deligne of a Hodge filtration on the de Rham cohomology of a exponentially twisted polarized variation of complex Hodge structure and prove a E_1 degeneration property for it.
• Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope
  
  • Baldoni Velleda
  • Berline Nicole
  • Vergne Michèle
  , 2008, pp.15-33. We extend to Barvinok's valuations the Euler-Maclaurin expansion formula which we obtained previously for the sum of values of a polynomial over the integral points of a rational polytope. This leads to an improvement of Barvinok's polynomial type algorithm for computing the highest coefficients of the corresponding Ehrhart quasi-polynomial. (10.1090/conm/452)
  DOI : 10.1090/conm/452
• Hommage à André Lichnerowicz (1915-1998)
  
  • Kosmann-Schwarzbach Yvette
  Gazette des Mathématiciens, Société Mathématique de France, 2008, 118, pp.52-56.