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
La géométrie riemannienne est un (peut-être le) chapitre central de la géométrie différentielle et de la géométriec ontemporaine en général. Le sujet est très riche et ce cours est une modeste introdu
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 introduce the student to the basic notion of analysis on metric (measure) spaces, quasiconformal mappings, potential theory on metric spaces, etc. The subjects covered wi
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
This is a standard course on Lie groups, Lie algebras and their representations.
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
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
The goal of this course is to help students learn the basic theory of complex manifolds and Hodge theory.
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
