Optimal Transport

What it is about

You will learn the foundations of the mathematical theory of Optimal Transport (OT). By the end you will understand central concepts such as Monge and Kantorovich formulations, the Wasserstein distances and their role in analysis, physics, economics and machine learning, as well as methods for handling high-dimensional, multi-criterion problems.

What you will be able to do

• Understanding of Monge and Kantorovich formulations of optimal transport
• Knowledge of Wasserstein distances and their topological properties
• Application of duality and weak convergence in OT problems
• Use of methods from convex geometry, variational analysis and PDEs
• Assessment of high-dimensional problems and strategies to overcome them
• Interpretation of concrete examples from economics, physics and machine learning

What the module consists of

• Lecture (4h/week)Introduction of relevant concepts and examples; preparation for autonomous literature work
• Practice sessions (2h/week)Deepening through weekly tasks, individual and group work with supervision and feedback

Teaching method

• Chalkboard lectureConcept and example delivery during lectures
• Weekly exercise groupsSolidification and verification of understanding through tasks, with increasing independence
• Provision of typed lecture materialsSelf-study and review; materials uploaded after each lecture
• Occasional projector/computer demonstrationsVisualization or computer work on individual topics