This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex
We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemann
The goal of this course is to help students learn the basic theory of complex manifolds and Hodge theory.
The subject deals with differential geometry and its relation to global analysis, partial differential equations, geometric measure theory and variational principles to name a few.
Smooth manifolds constitute a certain class of topological spaces which locally look like some Euclidean space R^n and on which one can do calculus. We introduce the key concepts of this subject, such
Calcul différentiel et intégral.
Eléments d'analyse complexe.
This course concerns modern bioanalytical techniques to investigate biomolecules both in vitro and in vivo, including recent methods to image, track and manipulate single molecules. We cover the basic
Après avoir traité la théorie de base des courbes et surfaces dans le plan et l'espace euclidien,
nous étudierons certains chapitres choisis : surfaces minimales, surfaces à courbure moyenne constante
This course will serve as a first introduction to the geometry of Riemannian manifolds, which form an indispensible tool in the modern fields of differential geometry, analysis and theoretical physics
This course will serve as a basic introduction to the mathematical theory of general relativity. We will cover topics including the formalism of Lorentzian geometry, the formulation of the initial val
