A wide range of topics in partial differential equations, complex analysis, and mathematical physics are presented to commemorate the memory of the great French mathematician Jean Leray. The 17 research articles are written by some of the world's leading mathematicians who explore important current subjects. Most articles contain complete proofs and excellent bibliographies. For graduate students and mathematical physicists as well as mathematicians in analysis and PDEs.

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Preface * Differential Forms, Cycles and Hodge Theory on Complex Analytic Spaces * On Exact Solutions of Linear PDEs * Necessary Conditions for Hyperbolic Systems * Monodromy of the Ramified Cauchy Problem * Non Linear Stability of an Expanding Universe with S^1 Isometry Group * On the Cauchy Problem for a Weakly Hyperbolic Operator: An Intermediate Case Between Effective Hyperbolicity and Levi Condition * Symplectic Path Intersections and the Leray Index * A Global Cauchy-Kowalewski Theorem in Some Gevrey Classes * Subriemannian Geometry and Subelliptic PDEs * On the Analytic Continuation of the Solution of the Cauchy Problem * Strong Gevrey Solvability for a System of Linear Partial Differential Equations * Spherically Symmetric Solutions of the Compressible Euler Equation * Hyperbolic Cauchy Problem Well Posed in the Class of Gevrey * Absence of Eigenvalues of Dirac Type Operators * The Behaviors of Singular Solutions of Partial Differential Equations in Some Class in the Complex Domain * Systèmes Uniformément Diagonalisables, Dimension Réduite et Symétrie II * On Hypoellipticity of the Operator exp [-|x_1|^{-\sigma }]D_1^2+x_1^4 D_2^2+1