Course teacher(s)
Andriy Haydys (Coordinator)ECTS credits
5
Language(s) of instruction
english
Course content
• Linear (pseudo)differential operators on manifolds;
• Sobolev spaces;
• Elliptic operators, the Laplace-Beltrami operator;
• Pseudodifferential operators and Fredholm property of linear elliptic operators;
• Hodge theory.
Objectives (and/or specific learning outcomes)
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.
Prerequisites and Corequisites
Required and Corequired knowledge and skills
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
Teaching methods and learning activities
• Lectures, including remote lecture on Teams if lecturing in person will not be possible.
References, bibliography, and recommended reading
R. Wells. Differential Analysis on Complex Manifolds.
F. Warner. Foundations of differentiable manifolds and Lie groups (Ch 4-6).
Contribution to the teaching profile
• To acquire advanced notions in certain areas of mathematics.
• Develop an abstraction process for the development of a theory.
• Write a mathematically rigorous solution or a result in a mathematical theory.
Other information
Additional information
It is intended to provide written lecture notes.
Contacts
Andriy Haydys, andriy.haydys@ulb.be
Campus
Plaine
Evaluation
Method(s) of evaluation
- Oral examination
Oral examination
Oral exam
Language(s) of evaluation
- english