Open (mathematical) problems in stellar dynamics

Stellar dynamics is a very old and much studied field of theoretical astrophysics, yet several core-problems are still unsolved or even not fully understood. In this talk I will illustrate a selection of such open problems, ranging from the construction of self gravitating figures of equilibrium strongly departing from spherical symmetry (in configuration space, through the Poisson equation, and in phase-space, by using the Collisionless Boltzmann Equation), to the long-term evolution of N-body systems.