Cesare Tronci visited the Mathematics Department at the University of Sheffield on Monday 24 March.  He gave a talk in the Differential Geometry Seminar on “The geometry of collisionless kinetic theories“.  An abstract follows: kinetic theories of multiparticle systems are dynamical continuum models governing the evolution of a probability density function on phase space. These theories are well known to possess a Lie-Poisson structure on the Poisson algebra of Hamiltonian functions. Recently, the statistical method of moments has been shown to possesses momentum map features conferring moments the same Lie algebra structure as the symbols of differential operators. The geometry underlying these structures involves coadjoint orbits on the group of strict contactomorphisms (aka quantomorphisms) of the prequantization bundle. This talk reviews recent progress on these topics and shows how certain moment closures produce integrable systems such as the Camassa-Holm equation on the diffeomorphism group and Bloch-Iserles system on the Jacobi group.   The link to the Differential Geometry Seminar page is here.