Introduction aux méthodes euclidiennes en théorie quantique des champs
Invariant analysis and contractions of symmetric spaces : part II
Invariant analysis and contractions of symmetric spaces. Part I
Invariant Differential Operators and Polynomials of Lie Transformation Groups.
Invariant differential operators in hyperbolic spaces.
Invariant Fourier Integral Operators on Lie Groups.
Invariant functions on Lie groups and Hamiltonian flows of surface group representations.
Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension
Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator associated to...
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
Invariant prolongation of BGG-operators in conformal geometry
BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The explicit calculation is presented in the case of conformal Killing forms.
Invariant Pseudo-Differential Operators.
Invariants de certaines actions de lie instabilité du caractère Fredholm.
Invariants homotopiques attachés aux fibrés symplectiques
On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne -orientée dans : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré -symplectique, c’est-à-dire dont le groupe structural est le revêtement à feuillets de . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...
Invariants intégraux fonctionnels pour des équations aux dérivées partielles d'origine géométrique
Invariants of characteristics of some systems of partial differential equations.
Inverse Scattering for Waveguides
We study the inverse scattering problem for a waveguide with cylindrical ends, , where each has a product type metric. We prove, that the physical scattering matrix, measured on just one of these ends, determines up to an isometry.
Inverse spectral results on even dimensional tori
Given a Hermitian line bundle over a flat torus , a connection on , and a function on , one associates a Schrödinger operator acting on sections of ; its spectrum is denoted . Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections , and we address the extent to which the spectrum determines the potential . With a genericity condition, we show that if the connection is invariant under...
Involutive distributions, invariant manifolds, and defining equations.
Involutive formulation and simulation for electroneutral microfluids
We study a microfluidic flow model where the movement of several charged species is coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...
Involutive formulation and simulation for electroneutral microfluids
We study a microfluidic flow model where the movement of several charged species is coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...