## Mathematical Physics Research Group

The Mathematical Physics Group studies problems arising from physics by rigorous mathematical methods.

A major question in this field concerns the rigorous derivation of effective macroscopic equations approximating the microscopic dynamics of many-body systems. Typical systems of interest in physics can indeed be described by models with a large number of components. The microscopic behaviour of such systems is driven by fundamental equations like the Newton or the SchrĂ¶dinger equation. Because of the huge number of particles, it is usually impossible to solve the fundamental equations and to analyse the system in terms of its elementary components. At the microscopic level, the behaviour of the particles appears to be extremely complicated. On the other hand, observers are interested in the collective behaviour of the system, arising on space and time scales which are much larger than the ones characterising the microscopic dynamics. On such macroscopic scales, the systems appear much simpler, and can be usually described by partial differential equations depending on a small number of degrees of freedom. The exact derivation of effective equations is one of the central problems of nonâ€“ equilibrium statistical mechanics and it is the focus of the Mathematical Physics Group, in particular in the framework of kinetic theory of gases.

In particular, the Mathematical Physics Group studies the derivation from many-body dynamics of the *Boltzmann equation* for rarefied gases, the *Hartree-Fock equation* for fermions, the *Vlasov-Poisson equation* for non-collisional plasmas, the *Landau equation* for collisional plasmas.

The research seminar of the Mathematical Physics Group takes place every week during the semester on Wednesdays at 14:15, jointly with the Analysis Group.

The BZ Seminar in Analysis, organised in collaboration with the University of Zurich and the ETH Zurich, takes place once per semester, alternating its location between Basel and Zurich.