MATS4310 Geometric inverse problems (5 cr)
Study level:
Advanced studies
Grading scale:
Pass - fail
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
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.
Completion methods
Written exercises and a short seminar presentation.
Assessment details
Passing the course requires 50 % of the exercise points and a short seminar presentation.
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
- 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
Description of prerequisites
MATS220 Functional analysis and MATS197 Differential geometry. Previous experience with Riemannian geometry, for instance from the course Geometry of geodesics, is also helpful.
Study materials
Parts of the upcoming textbook "Geometric inverse problems in two dimensions" by G. Paternain, M. Salo and G. Uhlmann.
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
x
Participation in teaching (5 cr)
Type:
Participation in teaching
Grading scale:
Pass - fail
Language:
English, Finnish