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 subject deals with differential geometry and its relation to global analysis, partial differential equations, geometric measure theory and variational principles to name a few.
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
This course assumes familiarity with beginning graduate level real analysis, complex analysis and functional analysis, and also basic
harmonic analysis, as well as fundamental concepts from differenti
The course provides an introduction to the study of curves and surfaces in Euclidean spaces. We will learn how we can apply ideas from differential and integral calculus and linear algebra in order to
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
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
Ce cours est une introduction à la géométrie différentielle classique des courbes et des surfaces, principalement dans le
plan et l'espace euclidien.
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 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
