Dear Colleagues, We would like to invite you to the following SPASS seminars, *Hamiltonian fluid models for plasmas in the presence of a strong guide field* by Emanuele Tassi (Observatoire de la Côte d'Azur), and *Transition densities for the 2d stochastic Navier-Stokes equations* by James Coe (University of Edinburgh), to be held consecutively on TUE 25.11.2025 at 14:00 and 15:00 CET in Sala Riunioni, Dipartimento di Matematica, UNIPI. A link for online participants will be shared on the website https://sites.google.com/unipi.it/spass Best, Francesco Grotto on behalf of the organizers ---------------------------------------------------------------- /Abstract (Tassi): Fluid models provide an effective tool for describing the dynamics of ionized gases such as plasmas. In particular, in some laboratory and astrophysical contexts (for instance, tokamak devices for thermonuclear fusion, or the solar wind) the dynamics of a plasma can be effectively described by means of fluid models assuming the presence of a dominant, constant in time, component of the magnetic field (strong guide field assumption). Several models of this kind have been derived and used for studying phenomena such as turbulence and magnetic reconnection. In the two-dimensional, non-dissipative limit, many of these models were shown to possess a reformulation in terms of advection equations for Lagrangian invariants. A paradigmatic example of this family of models consists of the two-field model derived by Schep, Pegoraro and Kuvshinov (Phys. Plasmas 1, 2843 (1994)). The formulation in terms of Lagrangian invariants is concomitant with the noncanonical Hamiltonian structure of these models.In this talk, I will show how the possibility of this reformulation and the existence of the corresponding noncanonical Hamiltonian structure can be traced back to the common origin of these models from a parent kinetic model of the so-called gyrokinetic, or drift-kinetic kind.With this approach, new Hamiltonian fluid models can also be derived, describing the evolution of an arbitrary number of Lagrangian invariants in two dimensions. Some general properties of models that can be derived by means of this approach will also be discussed. / /Abstract (Coe): We consider a family of 2d incompressible Navier-Stokes equations with Gaussian forcing that is white-in-time and coloured-in-space. We show that the laws of solutions at any given time are equivalent to those of the corresponding Ornstein-Uhlenbeck process, and in particular the invariant measures are equivalent.We establish a nonlinear version of the "time-shifted Girsanov method" of [Mattingly-Suidan, Mattingly-Romito-Su], enabling a direct comparison between the laws of nonlinear dissipative SPDEs. Then, exploiting the skew-symmetric structure of the Navier-Stokes nonlinearity, we construct a modified system that leaves the Gaussian measure invariant while remaining comparable to the Navier-Stokes dynamics. This talk is based on joint work with Martin Hairer and Leonardo Tolomeo. /