Geometry of Localized Effective Theories, Exact Semi-classical Approximation and the Algebraic Index

Spectral Geometry and the Semi-classical Approach

Analytic Geometry and Semi-classical Analysis

We study deformation theory for quantum integrable systems and prove several theorems concerning the Gevrey convergence and the unicity of perturbative expansions. À V.I. Arnold pour ses 70 ans.

Femtolensing: Beyond the Semi-Classical Approximation

Femtolensing is a gravitational lensing effect in which the magnification is a function not only of the positions and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of (10 − 10M⊙) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculati...

Semi-algebraic Geometry of Braid Groups

The braid group of n-strings is the group of homotopy types of movements of n distinct points in the 2-plane R. It was introduced by E. Artin [1] in 1926 in order to study knots in R. He gave a presentation of the braid group by generators and relations, which are, nowadays, called the Artin braid relations. Since then, not only in the study of knots, the braid groups appear in several contexts...

1 . New Algebraic Tools for Classical Geometry †

Classical geometry has emerged from efforts to codify perception of space and motion. With roots in ancient times, the great flowering of classical geometry was in the 19th century, when Euclidean, non-Euclidean and projective geometries were given precise mathematical formulations and the rich properties of geometric objects were explored. Though fundamental ideas of classical geometry are per...