NMAK18001U Analysis on Manifolds
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
Basic properties of differential operators on manifolds,
Relations between ellipticity and Fredholm properties.
Riemannian geometry, Levi - Civita connection and Laplace operator.
Dirac operators and properties of heat kernels
The student will obtain detailed understanding of the properties of elliptic differential operators on manifolds and their applications to topology and geometry.
At the end of the course the student will be able to prove basic properties of elliptic differential operators and demonstrate the ability to use them in applications.
The student will be able to use analysis of differenial operators on manifolds to study their topological and geometric properties.
Steve Rosenberg, "The Laplacian on a Riemannian Manifold" or equivalent textbook
Academic qualifications equivalent to a BSc degree is recommended.
- 7,5 ECTS
- Type of assessment
- Continuous assessment7 written assignments during the course of which the 5 best counts equally towards the final grade
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner.
Resubmission of all 7 assignments from the continuous assessment of which the 5 best counts equally towards the final grade. Deadline 12 Noon Friday in the reexamination week.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.