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Bardos Claude (Lab. J.L. Lions, Paris & WPI) & Mauser Norbert J. (WPI c/o U.Wien)  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Dec 16, 10:00 
Discussion of some open problems in many particle systems  
Discussion of history, methdods and open problems in mean field limits.  

Pickl Peter (U. Munich)  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Dec 16, 11:00 
Microscopic Derivation of the Vlasov equation  
The rigorous derivation of the Vlasov equation from Newtonian mechanics of N Coulombinteracting particles is still an open problem. In the talk I will present recent results, where an Ndependent cutoff is used to make the derivation possible. The cutoff is removed as the particle number goes to infinity. Our result holds for typical initial conditions, only. This is, however, not a technical assumption: one can in fact prove deviation from the Vlasov equation for special initial conditions for the system we consider.  

Saffirio Chiara (U. Zürich)  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Dec 16, 14:00 
Mean field evolution of fermions with Coulomb interaction  
We will consider the manybody evolution of initially confined fermions in a joint meanfield and semiclassical scaling, focusing on the case of Coulomb interaction. We will show that, for initial states close to Slater determinants and under some conditions on the solution of the timedependent HartreeFock equation, the manybody evolution converges towards the HartreeFock dynamics. This is a joint work with M. Porta, S. Rademacher and B. Schlein.  

Napiorkowski Marcin (IST, Austria)  WPI, OMP 1, Seminar Room 08.135  Thu, 15. Dec 16, 15:15 
Norm approximation for manybody quantum dynamics  
Starting from the manybody Schroedinger equation for bosons, I will discuss the rigorous derivation of the Hartree equation for the condensate and the Bogoliubov equation for the excited particles. The effective equations allows us to construct an approximation for the manybody wave function in norm. This talk is based on joint works with Phan Thanh Nam.  

Jabin PierreEmmanuel (U. Maryland)  WPI, OMP 1, Seminar Room 08.135  Fri, 16. Dec 16, 9:30 
Mean field limits for 1st order systems with bounded stream functions  
We consider a large systems of first order coupled equations. The system model the interaction ofdiffusive particles through a very rough force field, which can be the derivative of a bounded stream function. Through a new, modified law of large numbers, we are able to give quantitative estimates between any statistical marginal of the discrete solution and the mean field limit. We are also able to extend the method to cover the case of the 2d incompressible NavierStokes system in the vorticity formulation.  

Ayi Nathalie (U.Nice & INRIA)  WPI, OMP 1, Seminar Room 08.135  Fri, 16. Dec 16, 10:45 
From Newton's law to the linear Boltzmann equation without cutoff  
We provide a rigorous derivation of the linear Boltzmann equation without cutoff starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the BoltzmannGrad scaling. The main difficulty in this context is that, due to the infinite range of the potential, a nonintegrable singularity appears in the angular collision kernel, making no longer valid the singleuse of Lanford's strategy. On this talk, I will present how a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and SaintRaymond to study the collision process and of new duality arguments to study the additional terms associated with the infinite range interaction (leading to some explicit weak estimates) overcomes this difficulty.  

Golse François (Ecole polytechnique, Paris)  WPI, OMP 1, Seminar Room 08.135  Fri, 16. Dec 16, 14:00 
Quantization of probability densities : a gradient flow approach  
Quantization of probability densities on the Euclidean space refers to the approximation of a probability measure that is absolutely continuous with respect to the Lebesgue measure by convex combination of Dirac measures. The quality of the approximation is measured in terms of a distance metrizing the weak convergence of probability measures, typically a MongeKantorovich (or Vasershtein) distance. The talk with describe a gradient flow approach to the quantization problem in the limit as the number of points goes to infinity. (Work in collaboration with E. Caglioti and M. Iacobelli).  

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