Publications

2008

• 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.
• 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
• An elementary proof of Blundon's inequality
  
  • Dospinescu Gabriel
  • Lascu Mircea
  • Pohoata Cosmin
  • Tetiva Marian
  Journal of Inequalities in Pure and Applied Mathematics, School of Communications and Informatics, 2008, 9 (4), pp.Article 100. In this note, we give an elementary proof of Blundon's Inequality. We make use of a simple auxiliary result, provable by only using the Arithmetic Mean - Geometric Mean Inequality.
• On some completions of the space of Hamiltonian maps
  
  • Humilière Vincent
  Bulletin de la société mathématique de France, Société Mathématique de France, 2008, 136 (3), pp.373-404. We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, we give a convergence criterion for these distances. This allows us to prove that the completions contain non-ordinary elements, as for example, discontinuous Hamiltonians. We also prove that some dynamical properties of Hamiltonian systems are preserved in the completions.
• Pseudodifferential operators and weighted normed symbol spaces.
  
  • Sjostrand Johannes
  Serdica Mathematical Journal, Bulgarian Academy of Sciences, Institute of Mathematics, 2008, pp.1-38.
• Modular classes of Lie algebroid morphisms
  
  • Kosmann-Schwarzbach Yvette
  • Laurent-Gengoux Camille
  • Weinstein Alan
  Transformation Groups, Springer Verlag, 2008, 13 (3-4), pp.727-755. We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms associated to Lie algebroid extensions. We also define generalized morphisms, including Morita equivalences, that act on the 1-cohomology, and observe that the relative modular class is a coboundary on the category of Lie algebroids and generalized morphisms with values in the 1-cohomology. (10.1007/s00031-008-9032-y)
  DOI : 10.1007/s00031-008-9032-y