Pour tout renseignement complémentaire, veuillez contacter les
organisateurs, Hakim
Boumaza, Mathieu
Lewin
ou Stéphane
Nonnenmacher.
| 14h - 15h | Annalaura Stingo (Ecole Polytechnique) |
Global stability of the Kaluza-Klein theories Abstract: The Kaluza-Klein theories represent the classical mathematical approach to the unification of general relativity with electromagnetism and more generally with gauge fields. In these theories, general relativity is considered in 1+3+d dimensions and in the simplest case d=1 dimensional gravity is compactified on a circle to obtain at low energies a (3+1)-dimensional Einstein-Maxwell-Scalar systems. In this talk I will discuss the problem of the classical global stability of Kaluza-Klein theories when d=1. This is a joint work with C. Huneau and Z. Wyatt. |
| 15h15 - 16h15 | Julien Ricaud (Ecole Polytechnique) |
Spectral stability in the nonlinear Dirac equation with Soler-type nonlinearity Abstract: This talk concerns the (generalized) Soler model: a nonlinear (massive) Dirac equation with a nonlinearity taking the form of a space dependent mass. The equation admits standing wave solutions and they are generally expected to be stable (i.e., small perturbations in the initial conditions stay small) based on numerical simulations. However, contrarily to the nonlinear Schrödinger equation for example, there are very few results in this direction. The results that I will discuss concern the simpler question of spectral stability (and instability), i.e., the absence (or presence) of exponentially growing solutions to the linearized equation around a solitary wave. As in the case of the nonlinear Schrödinger equation, this is equivalent to the presence or absence of "unstable eigenvalues" of a non-selfadjoint operator with a particular block structure. I will highlight the differences and similarities with the Schrödinger case, present some results for the one-dimensional case, and discuss open problems. This is joint work with Danko Aldunate, Edgardo Stockmeyer, and Hanne Van Den Bosch. |