These two volumes constitute the Proceedings of the `Conférence Moshé Flato, 1999'. Their spectrum is wide but the various areas covered are, in fact, strongly interwoven by a common denominator, the unique personality and creativity of the scientist in whose honor the Conference was held, and the far-reaching vision that underlies his scientific activity. With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics. Volume I is prefaced by reminiscences of and tributes to Flato's life and work. It also includes a section on the applications of sciences to insurance and finance, an area which was of interest to Flato before it became fashionable. The bulk of both volumes is on physical mathematics, where the reader will find these ingredients in various combinations, fundamental mathematical developments based on them, and challenging interpretations of physical phenomena. Audience: These volumes will be of interest to researchers and graduate students in a variety of domains, ranging from abstract mathematics to theoretical physics and other applications. Some parts will be accessible to proficient undergraduate students, and even to persons with a minimum of scientific knowledge but enough curiosity.
Volume I: Preface. I. Moshé Flato, the man and the scientist. Program of the inaugural meeting. Speeches and Messages. Moshé's Memoirs; D. Sternheimer. In retrospect: A personal view on Moshé Flato's scientific legacy; D. Sternheimer. Curriculum vitae of Moshé Flato. The publications of Moshé Flato. II. Applications ofsciences to insurance and finance. Program. Le Conseil scientifique de l'UAP et ses réalisations; Y. Chassagne. A new method for optimal equity allocation and portfolio selection; E. Taflin. The recognition of handwriting; J.-C. Simon. From Bachelier and Lundberg to insurance and weather derivatives; H. Geman.III. Quantization,deformations, and symmetries. On the Bohr-Rosenfeld measurability problem for non-linear systems; Y. Aharonov, B. Reznik. Star-produits et star-algèbres holomorphes; L.B. de Monvel. Cyclic cohomology and Hopf algebra symmetry; A. Connes, H. Moscovici. Modular double of a quantum group; L. Faddeev. On G-trace and G-index in deformation quantization; B. Fedosov. Superconformal field theories, multiplet shortening, and the AdS_{s}/SCFT_{4} correspondence; S.Ferrara, A. Zaffaroni. On a classical limit of quantum theory and the non-linear Hartree equation; J. Fröhlich, et al. Singletons and neutrinos; C. Frønsdal. Variations on deformation quantization; S. Gutt. Deformations of algebras over operads and the Deligne conjecture; M. Kontsevich, Y. Soibelman. A generalization of the Bott-Borel-Weil theorem and Euler number multiplets of representations; B. Kostant. Self-energy of electrons in non-perturbative QED; E. Lieb, M. Loss. Nonlinear relativistic evolution equations: Survey of a new approach; J.C.H. Simon, E.Taflin. Quantum field theories on an algebraic curve; L.A. Takhtajan. Program of the conference. List of participants. Committees. Index. Volume II.IV. Contributed papers. Singletons on AdS_{n}; E.Angelopoulos, M. Laoues. Remarks on the zeta-regularized determinant of differential operators; A. Asada. Projectable star-products; S.A.Lares. The deformation quantization of certain super-Poisson brackets and BRST cohomology; M. Bordemann. On positive deformations of ★-algebras; H. Bursztyn, S. Waldmann. Symmetric symplectic spaces with Ricci-type curvature; M. Cahen, et al. Drinfeld realization of quantum superalgebras and U_{q} (ošp(1,2)); J. Ding, B. Feigin. Quantum homogeneous spaces and quasi-Hopf algebras; B. Enriquez, Y. Kosmann-Schwarzbach. Gauged q-fields; R.Finkelstein. Generalized coherent states for arbitrary quantum systems; J.-P. Gazeau, P. Monceau. Tensor products of Frobenius manifolds and moduli spaces of higher spin curves; T.J. Jarvis, et al. On Fedosov's approach to deformation quantization with separation of variables; A.V. Karabegov. The Master thesis of Moshé Flato; M.Kibler. Anticipative Chen-Souriau cohomology and Hochschild cohomology; R. Léandre. Are there macroscopic quantum bodies? B. Mielnik. Star-products, spectral analysis, and hyperfunctions; C.Moreno, J.A.P. da Silva. Induced action in QCD; V. Novozhilov, Y.Novozhilov. Deformation quantization of Fréchet-Poisson algebras: Convergence of the Moyal product; H. Omori, et al. On the deformation aspects of the replica thermalisation of the SU(2)-invariant Thirring model; M. Pillin. Improved perturbation expansion in quantum chromodynamics; P. Rączka. Deformation quantization of Lagrangian fiber bundles; N. Reshetikhin, M. Yakimov. Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization; M. Schlichenmaier. Homotopy Gerstenhaber algebras; A.A. Voronov. Linearization problems for Lie algebroids and Lie groupoids; A. Weinstein. Appendix A: Program of the scientific conference. Appendix B: Table of contents of volume I. Index.