MATS423 Optimal Mass Transportation (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023
Description
Monge and Kantorovitch formulations of optimal mass transportation, existence and uniqueness of optimal transport maps, Wasserstein distance, and brief introduction to functionals on Wasserstein spaces. Optionally applications of optimal mass transportation.
Learning outcomes
The student is able to formulate the optimal mass transportation problem and prove the existence of its solution under suitable assumptions.
Description of prerequisites
Measure and integration theory 1 and 2
The courses Functional analysis, Real analysis and Advanced measure theory will be useful but not mandatory.
Study materials
lecture notes
Literature
- http://cvgmt.sns.it/paper/195/
- C. Villani, Optimal Transportation - Old and New
Completion methods
Method 1
Evaluation criteria:
course exam points and exercise points
Select all marked parts
Method 2
Evaluation criteria:
final exam points
Select all marked parts
Parts of the completion methods
x
Participation in teaching (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
course exam points and exercise points
Language:
English, Finnish
Study methods:
lectures and exercises
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
final exam points
Language:
English, Finnish