Publications

2008

• 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
• 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.
• 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.
• 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.
• 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
• 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.
• 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
• 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.
• Pseudodifferential operators and weighted normed symbol spaces.
  
  • Sjostrand Johannes
  Serdica Mathematical Journal, Bulgarian Academy of Sciences, Institute of Mathematics, 2008, pp.1-38.