241246 Optimal transport and Applications (S) (WiSe 2022/2023)

The fundamental question in the theory of optimal mass transportation is the following. For any given initial and final probability measures, we are searching for the minimization of the total transportation cost, where the initial probability measure is transformed into the given final one. While the problem dates back to the 18th century, the first satisfactory solution, even in the Euclidean setting, was provided only in the late 20th century.

The field of optimal mass transportation has developed into a rich and powerful theory providing fruitful questions and results both within the theory itself and in applications. The aim of this seminar is to cover the fundamentals of the optimal transport theory, and then proceed to applications. The specific topics and direction of application will be tailored to match the level and interest of participants.

Contact:
Matthias Erbar, erbar@math.uni-bielefeld.de
Timo Schulz, timo.schultz@math.uni-bielefeld.de
Zihui He, zihui.he@uni-bielefeld.de

Requirements for participation, required level

The seminar is intended for advanced bachelor or master students. Ph.D. students and postdocs are also welcome. Solid background in measure theory is required.

Bibliography

References:
[Vil03] C. Villani. Topics in optimal transportation. Vol. 58. Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2003, pp. xvi+370.

[San15] F. Santambrogio. Optimal transport for applied mathematicians. Vol. 87. Progress in Nonlinear Differential Equations and their Applications. Calculus of variations, PDEs, and modeling. Birkhäuser/Springer, Cham, 2015, pp. xxvii+353.