The classical description of nucleation of cavities in a stretched fluid relies on a one-dimensional Fokker-Planck equation (FPE) in the space of their sizes, with the diffusion coefficient  constructed from macroscopic hydrodynamics and thermodynamics, as shown by Zeldovich. When additional variables (e.g., vapor pressure) are required to describe the state of a bubble, a similar approach to construct a diffusion tensor  generally works only in the direct vicinity of the thermodynamic saddle point corresponding to the critical nucleus. We show, nevertheless, that “proper” kinetic variables to describe a cavity can be selected, allowing to introduce a diffusion tensor in the entire domain of parameters. In this way, for the first time, complete FPE’s are constructed for viscous volatile and inertial fluids. 

We review recent results on higher-dimensional quasiperiodic (singular) cocycles.

We generalize well known properties of points of order 3 on elliptic curves to the case of torsion points of order 2g+1 on genus g hyperelliptic curves. This is a report on a joint work with Boris Bekker (StPetersburg).