Lecturer: Professor François Golse (École polytechnique, CMLS)

Homepage: https://www.cmls.polytechnique.fr/perso/golse/

Title: Quantum Wasserstein “Metric” and Applications

Abstract: The theory of optimal transport, initiated by Monge in 1781, and continued by Kantorovich in 1942, has become a flourishing branch of the calculus of variations, with striking

applications in a great variety of fields (statistical mechanics, nonlinear PDEs, machine

learning…) Optimal transport provides us with powerful tools aimed at discriminating

between two (Borel) probability measures on a Euclidean space. The purpose of these

lectures is

(1) to recall the basics of classical optimal transport,

(2) to introduce a similar theory for density operators, which are the quantum analogue ofprobability measures on the classical phase space, and

(3) to present some applications of this new theory.

These lectures are based on various joint works with E. Caglioti, S. Jin, C. Mouhot and T. Paul.

Lecture notes: Lecture 1, Lecture 2, Lecture 3. 

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Lecturer: Professor Claude Bardos (Paris Diderot University, France)

Homepage: https://www.ljll.fr/~bardos/

Title: Qualitative behaviour of the Vlasov Poisson dynamics

Abstract: The lecture will study the Vlasov Poisson dynamics in both stable and unstable regime, which surprisingly intimately links to the quasilinear theory, diffusion limit, and wave turbulence theory.

Lecture notes: TBA 

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Lecturer: Dr. Trinh T. Nguyen (University of Wisconsin at Madison, USA)

Homepage: https://sites.google.com/view/tnguyen65/home

Title: An introduction to Boltzmann equations and hydrodynamic limits 

Abstract: This mini course provides an introduction to the theory of Boltzmann equations. Key topics include the existence of solutions, asymptotic behavior near Maxwellian equilibrium, and the hydrodynamic limits. Formal derivations of fluid equations using the Hilbert expansion will be presented, illustrating how macroscopic fluid dynamics emerge from the Boltzmann kinetic equation.

Lecture notes: TBA