Global analysis

•    Linear (pseudo)differential operators on manifolds;
•    Sobolev spaces;
•    Elliptic operators, the Laplace-Beltrami operator;
•    Classical (co)homology theories (in particular, de Rham cohomology, singular homology);
•    Hodge theory. 

The central topic of the course is the interplay between geometry, topology, and analysis. It turns out that elliptic differential operators on manifolds capture subtle information about the underlying space. For example, the dimension of the kernel of the Hodge Laplacian depends only on the topology of the underlying manifold. The aim of the course is to provide a glimpse in this exciting area of mathematics.

Connaissances et compétences pré-requises ou co-requises

MATH-F410  Differential geometry II    

The following courses may be helpful but are not necessarily required:

MATH-F419 Algebraic topology
MATH-F412 Méthodes variationnelles et équations aux dérivées partielles
 

Cours co-requis

•    Lectures, including remote lecture on Teams if lecturing in person will not be possible.

Références, bibliographie et lectures recommandées

F. Warner. Foundations of differentiable manifolds and Lie groups (Ch 4-6).

Informations complémentaires

It is intended to provide written lecture notes. 

Contacts

Andriy Haydys, andriy.haydys@ulb.be

Campus

Plaine

Méthode(s) d'évaluation

• Examen oral

Examen oral

examen oral

Langue(s) d'évaluation

• anglais