The spectrum of the Laplace operator on conformally flat manifolds
The spectrum of the Laplacian on the warped products of Riemannian manifolds.
The spectrum of the symmetric space SP()/SU().
The Srní lectures on non-integrable geometries with torsion
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...
The State Space of the K0-group of a Simple Separable C*-algebra.
The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial
The symbol of a function of a pseudo-differential operator
We give an explicit formula for the symbol of a function of an operator. Given a pseudo-differential operator on with symbol and a smooth function , we obtain the symbol of in terms of . As an application, Bohr-Sommerfeld quantization rules are explicitly calculated at order 4 in .
The symbol of a lagrangian distribution
The symmetry of minimizing harmonic maps from a two dimensional domain to the sphere
The trace of the generalized harmonic oscillator
We study a geometric generalization of the time-dependent Schrödinger equation for the harmonic oscillatorwhere is the Laplace-Beltrami operator with respect to a “scattering metric” on a compact manifold with boundary (the class of scattering metrics is a generalization of asymptotically Euclidean metrics on , radially compactified to the ball) and is a perturbation of , with a boundary defining function for (e.g. in the compactified Euclidean case). Using the quadratic-scattering...
The transmission property.
The two-dimensional eikonal equation.
The verification of the Nirenberg-Treves conjecture
In a series of recent papers, Nils Dencker proves that condition implies the local solvability of principal type pseudodifferential operators (with loss of derivatives for all positive ), verifying the last part of the Nirenberg-Treves conjecture, formulated in 1971. The origin of this question goes back to the Hans Lewy counterexample, published in 1957. In this text, we follow the pattern of Dencker’s papers, and we provide a proof of local solvability with a loss of derivatives.
The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds
The wave map problem. Small data critical regularity
The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory. As a consequence,...
The weak type L1 convergence of eigenfunction expansions for pseudodifferential operators.
The Yang-Mills equations and the topology of 4-manifolds
Théorème des résidus asymptotique pour le mouvement brownien sur une surface riemannienne compacte
Théorèmes de dualité globale pour les Dx-modules cohérents.
Théorie des opérateurs différentiels gradués sur les formes différentielles