Introduction aux problèmes analytiques posés par le système des équations de Yang-Mills
Introduction to algebra over “brave new rings”
Introduction to cochains of differential operators
Introduction to constructive quantum field theory
Introduction to Grassmann manifolds and quantum computation.
Introduction to magnetic resonance imaging for mathematicians
The basic concepts and models used in the study of nuclear magnetic resonance are introduced. A simple imaging experiment is described, as well as, the reduction of the problem of selective excitation to a classical problem in inverse scattering.
Introduction to noncommutative differential geometry.
Introduction to quantum Lie algebras
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras . The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of .
Invariant measures for the defocusing Nonlinear Schrödinger equation
We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane . We also prove an estimate giving some intuition to what may happen in dimensions.
Invariant states on Borchers' tensor algebra
Invariant subspaces for the Schrödinger evolution group
Invariant symbolic calculus for compact Lie groups
We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.
Invariant symbolic calculus for semidirect products
Let be the semidirect product where is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space . Let be a unitary irreducible representation of which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of whose little group is a maximal compact subgroup of . We construct an invariant symbolic calculus for , under some technical hypothesis. We give some examples including the Poincaré group.
Invariants of 3-manifolds via link polynomials and quantum groups.
Invariants of three-manifolds, unitary representations of the mapping class group, and numerical calculations.
Inverse scattering problems in several dimensions
Inverse scattering theory for Dirac operators
Invertible cohomological field theories and Weil-Petersson volumes
We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....
Irreducible holonomy representations
Irreversibility in quantum mechanics.