Kurs Mathematisches Seminar

Absolventenseminar

Optimal Transport and Mean Field Games are two interconnected mathematical

frameworks with wide-ranging applications in economics, physics, and

machine learning. Optimal Transport, pioneered by mathematician Leonid

Kantorovich, addresses the problem of efficiently transporting goods from

one location to another, minimizing the associated cost. It has

applications in logistics, image processing, and even neuroscience.

Mean Field Games, developed by Jean-Michel Lasry and Pierre-Louis Lions,

extend this concept to dynamic systems with a large number of agents. It

models the strategic interactions of individuals in a society or economy,

seeking to find equilibrium solutions. This approach has profound

implications in economics, where it can model market behavior, traffic

flow, and pricing strategies.

Together, these fields merge to tackle complex problems involving the

collective behavior of agents and the optimal allocation of resources. They

find applications in diverse areas, from urban planning and traffic

management to understanding the dynamics of financial markets and the

behavior of particles in physics. As research continues to advance, Optimal

Transport and Mean Field Games promise innovative solutions to real-world

challenges.

Time + location: information available on

https://page.math.tu-berlin.de/~friz/ (Link Student Info)

Prerequisites: measure theory, analysis, probability theory (at least at

the level of WT2, TUB)

References:

  -

  Figalli, Alessio, and Federico Glaudo. An invitation to optimal

  transport, Wasserstein distances, and gradient flows. 2021.

  -

  Notes on Mean Field Games (from P.-L. Lions’ lectures at Coll`ege de

  France) Pierre Cardaliaguet, notes available

https://www.ceremade.dauphine.fr/~cardaliaguet/MFG20130420.pdf

  -

  A. Figalli An Introduction to Optimal Transport and Wasserstein Gradient

  Flows, lectures notes available

  https://people.math.ethz.ch/~afigalli/lecture-notes-pdf/An-introduction-to-optimal-transport-and-Wasserstein-gradient-flows.pdf

Rene Carmona, Francois Delarue, Probabilistic Analysis of Mean-Field Games,

https://arxiv.org/abs/1210.5780