The 17 invited research articles in this volume, all written by §leading experts in their respective fields, are dedicated to the great §French mathematician Jean Leray. A wide range of topics with §significant new results---detailed proofs---are presented in the areas §of partial differential equations, complex analysis, and mathematical §physics. §Key subjects are: §Treated from the mathematical physics viewpoint: nonlinear stability §of an expanding universe, the compressible Euler equation, spin groups §and the Leray--Maslov index, §Linked to the Cauchy problem: an intermediate case between effective §hyperbolicity and the Levi condition, global Cauchy--Kowalewski §theorem in some Gevrey classes, the analytic continuation of the §solution, necessary conditions for hyperbolic systems, well posedness §in the Gevrey class, uniformly diagonalizable systems and reduced §dimension, and monodromy of ramified Cauchy problem. §Additional articles examine results on: §Local solvability for a system of partial differential operators, §The hypoellipticity of second order operators, Differential forms §and Hodge theory on analytic spaces, Subelliptic operators and sub- §Riemannian geometry. §Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet- §Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano, B. §Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M. Mechab, K. §Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y. Ohya, T. Okaji, §S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi §The book is suitable as a reference text for graduate students and §active researchers.
