MATS4310 Geometric inverse problems (5 cr)
Learning outcomes
After taking the course the student
- is familiar with basic properties of geodesic X-ray transforms
- is able to use tools related to transport equations to study geodesic X-ray transforms
- recognises different geometric inverse problems and knows related uniqueness results
Study methods
Written exercises and a short seminar presentation.
Content
The Radon transform in the plane, geodesic X-ray transforms on manifolds with boundary, regularity and uniqueness results for related transport equations, boundary rigidity.
Materials
Parts of the upcoming textbook "Geometric inverse problems in two dimensions" by G. Paternain, M. Salo and G. Uhlmann.
Assessment criteria
Passing the course requires 50 % of the exercise points and a short seminar presentation.
Prerequisites
MATS220 Functional analysis and MATS197 Differential geometry. Previous experience with Riemannian geometry, for instance from the course Geometry of geodesics, is also helpful.