MATS226 Quasiconformal Mappings in the Plane (9 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028
Description
The basic theory of quasiconformal mappings in the plane, including connections to various fields such as harmonic analysis and partial differential equations. Central topics include the Beltrami equation, Beurling transform, measurable Riemann mapping theorem, and regularity of quasiconformal mappings.
Learning outcomes
The students know the definition and basic properties of quasiconformal mappings in the plane and they are familiar with characteristic aspects of the planar theory, such as the measurable Riemann mapping theorem. The students also learn how the theory is connected to other fields of mathematics.
Description of prerequisites
Measure and integration theory 1 and 2, Complex analysis 1 and 2
Literature
- Astala, K., Iwaniec, T., Martin, G.: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane.
Completion methods
Method 1
Evaluation criteria:
points from exercises and/or seminar presentation and/or exam, depending on the implementation of the course
Select all marked parts
Method 2
Evaluation criteria:
final exam points
Select all marked parts
Parts of the completion methods
x
Participation in teaching (9 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
points from exercises and/or seminar presentation and/or exam, depending on the implementation of the course
Language:
English, Finnish
Study methods:
lectures and exercises
x
Exam (9 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
final exam points
Language:
English, Finnish