Jean Leray '99 Conference Proceedings

I: Hyperbolic Systems and Equations.- Caractère holonôme d'une solution élémentaire.- Necessary conditions for hyperbolicity of first order systems.- On the Cauchy problem for hyperbolic operators with non-regular coefficients.- Multiple points of the characteristic manifold of a diagonalizable operator.- Large temps de vie des solutions d'un problème de Cauchy non linéaire.- Une remarque sur un prolongement analytique de la solution du problème de Cauchy.- Conormality and lagrangian properties along diffractive rays.- Caractérisation des opérateurs différentiels hyperboliques.- A dependence domain for a class of micro-differential equations with involutive double characteristics.- Ramification non abélienne.- II: Symplectic Mechanics and Geometry.- Extension du calcul différentiel et application à la théorie des groupes de Lie en dimension infinite.- The cohomological meaning of Maslov's lagrangian path intersection index.- A Kähler structure on the punctured cotangent bundle of the Cayley projective plane.- On mechanical systems with a Lie group as configuration space.- Dirac fields on asymptotically simple space-times.- An embedding result for some general symbol classes in the Weyl calculus.- The lagrangian in symplectic mechanics.- Geometry of solution spaces of spaces of Yang-Mills equations.- III: Sheaves and Spectral Sequences.- La theórie des résidus sur un espace analytique complexe.- Derivation of exact triples and Leray-Koszul spectral sequences.- IV: Elliptic Operators; Index Theory.- Le noyau de la chaleur des opérateurs sous-elliptiques des groupes d'Heisenberg.- The geometry of Cauchy data spaces.- On the Cauchy problem for Kirchhoff equations of p-laplacian type.- A remark on surgery in index theory of elliptic operators.- Theq invariant and elliptic operators in subspaces.- Regularisation of mixed boundary problems.- V: Mathematical Physics.- Covariant method for solution of Cauchy's problem based on Lie group analysis and Leray's form.- Liouville forms, parallelisms and Cartan connections.- A two-dimensional non-linear shell model of Koiter's type.- A model of the process of thinking based on the dynamics of bundles of branches and sets of bundles of p-adic trees.- Global wave maps on black holes.- Entanglement, parataxy, and cosmology.- Sur le contrôle des équations de Navier-Stokes.- Addresses.