Stable self-similar blow-up dynamics for slightly $L^2$-supercritical generalized KdV equations
Séminaire Laurent Schwartz — EDP et applications
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On blow-up and dynamics near ground states for some semilinear equations
Séminaire Laurent Schwartz — EDP et applications
Solutions of type 2 with two bubble for critical nonlinear wave equations
Séminaire Laurent Schwartz — EDP et applications
Global dynamics for the nonlinear Schrödinger equation with a potential
Mini-cours, 1ère partie
Global dynamics for the nonlinear Schrödinger equation with a potential
Mini-cours, 2ème partie
Motivic cohomology of formal schemes in characteristic p
The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.
Notes on the local p-adic Simpson correspondence
The local p-adic Simpson correspondence by Faltings asserts that there is a natural equivalence of categories between small generalized representations and small Higgs modules for an affine semi-stable scheme over a complete discrete valuation ring of mixed characteristic with algebraically closed residue field. However, in the case of rational coefficients, the construction of the functor from the former to the latter, reducing to the theory for integral coefficients, does not seem to work as it is written, as pointed out by Ahmed Abbes. In this talk, I give an alternative argument based on a generalized Sen's theory for the semi-stable scheme and complete the local theory for rational coefficients.
Sur la conjecture de Langlands locale pour les groupes classiques en caractéristique p
On expose les résultats récents sur la conjecture de Langlands locale pour les groupes classiques en caractéristique p, et les techniques de théorie des représentations utilisées. Nous commençons avec le cas d'une représentation générique. On discute les fonctions L et les facteurs locaux sur un corps local non archimédien. Nous présentons les résultats de Ganapathy-Varma sur le transfert de la caractéristique zéro à la caractéristique p pour les groupes classiques deployés. Nous donnons aussi une autre approche du global au local en collaboration avec Gan pour les groupes classiques quasi-deployés. Nous faisons une conjecture dans le cas général, mais le cas générique est complet. Nous donnons des détails pour l'étude des fonctions L avec la méthode de Langlands-Shahidi.
Dynamics of the focusing critical wave equation in the nonradial case
Two dimensional water waves in holomorphic coordinates
Boundary layer separation for the stationary Prandtl equation
Mini-cours
Gravitational Waves and Binary Black Holes
This talk will comprise two parts. A first part will be a (colloquium-style) presentation of the main physical aspects of the recent observation by LIGO of a gravitational-wave signal interpreted as coming from the coalescence of two black holes. The second part will explain in some detail the theoretical-physics methods that have been used to solve the (PDE) problem of the motion and gravitational radiation of a system of two coalescing black holes.
