The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also discussed on the basis of the analytical solution of the wave kinetic equation specific to Gaussian beams of electromagnetic waves propagating in a ``lens-like'' medium for which the complex geometrical optics solution is already available.Comment: Extended version comprising two new section

Toric moment mappings and Riemannian structures

Coadjoint orbits for the group SO(6) parametrize Riemannian G-reductions in six dimensions, and we use this correspondence to interpret symplectic fibrations between these orbits, and to analyse moment polytopes associated to the standard Hamiltonian torus action on the coadjoint orbits. The theory is then applied to describe so-called intrinsic torsion varieties of Riemannian structures on the Iwasawa manifold.Comment: 25 pages, 14 figures; Geometriae Dedicata 2012, Toric moment mappings and Riemannian structures, available at http://www.springerlink.com/content/yn86k22mv18p8ku2

The inception of Symplectic Geometry: the works of Lagrange and Poisson during the years 1808-1810

The concept of a symplectic structure first appeared in the works of Lagrange on the so-called "method of variation of the constants". These works are presented, together with those of Poisson, who first defined the composition law called today the "Poisson bracket". The method of variation of the constants is presented using today's mathematical concepts and notations.Comment: Presented at the meeting "Poisson 2008" in Lausanne, July 2008. Published in Letters in Mathematical Physics. 22 page

Cohomology of GKM Fiber Bundles

The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are both GKM and derive a graph theoretical version of the Leray-Hirsch theorem. Then we apply this result to the equivariant cohomology theory of flag varieties.Comment: The paper has been accepted by the Journal of Algebraic Combinatorics. The final publication is available at springerlink.co

Du calvinisme au jansénisme : des convertis du Grand Siècle

Isaac Papin et Marin Groteste Desmahis sont deux convertis du Grand Siècle. Cet article étudie leurs parcours croisés, du calvinisme au jansénisme