Solving the evolution equation for an interacting N-particle system analytically or numerically is, in many cases, very difficult or even impossible. However, there are situations where the correlations between the particles are negligible. In many such cases it is possible to give an effective one-particle descriptions which explains most of the physics, and to proof the validity of this effective description with mathematical rigor when N goes to infinity ("derive the equation"). One of the most basic systems one can think of is the dynamics of N stars forming a galaxy, interacting via gravitation. The effective one particle description one expects to be valid is the Vlasov equation. Deriving the Vlasov equation for this system is, however, still an open problem: the technical difficulty comes from the singularity of the interaction. In the talk I will present recent results where the interaction is slightly changed by an N-dependent cutoff.
Peter Pickl studied physics and mathematics at Ludwig-Maximilians University in Mu?nchen (LMU) and finished his Ph.D. in mathematics in 2005. The title of his thesis was Existence of Spontaneous Pair Creation. He spent several years of postdoc in Tu?bingen, Vienna and Zu?rich working in the groups of Stefan Teufel, Jakob Yngvason and Ju?rg Fr?hlich. Since 2010 he is a Professor at the mathematical institute at LMU and since April 2018 Visiting Professor of the recently founded Duke Kunshan University. His research area is mathematical physics with a focus on the effective description of many body systems.