Winter term 2024/25 Lecture Optimal Transport and Applications

Announcement

Scope: Optimal Transport (OT) is an exciting field at the intersection of Probability Theory, Geometry, and Partial Differential Equations (PDEs). It provides a framework to compare probability distributions by finding a path between them that minimizes a certain cost or energy functional. This interdisciplinary subject has found numerous applications in the theory of PDEs, probability theory, and machine learning. In this course, we will delve into the fundamental theory of Optimal Transport, explore applications, and discuss numerical methods to solve OT problems effectively. The course is aimed at students with diverse backgrounds who intend to specialize in Applied Analysis, Probability Theory, Optimization, or Machine Learning.

The Moodle page contains the exercise sheets and the script.

Prerequisites: Functional analysis

Hours per term: 2+1 SWS

Literature

  • Optimal Transport for Applied Mathematicians, Filippo Santambrogio, Springer 2015 Link
  • Optimal Transpport: Old and New, Cedric Villani, Springer, 2009 Link
  • Computational Optimal Transport, Gabriel Peyré and Marco Cuturi, 2018, arXiv Link
  • Gradient Flows in Metric Spaces and the Space of Probability measures, Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré, Springer, 2008, Link