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:
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Figalli, Alessio, and Federico Glaudo. An invitation to optimal
transport, Wasserstein distances, and gradient flows. 2021.
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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
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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
