The project is aimed at investigating qualitative properties of stochastic infinite dimensional systems (in particular, stochastic partial differential equations) and at research in infinite dimensional stochastic control theory. More specifically, the following topics will be emphasized: 1. Investigation of stochastic nonlinear wave equations, especially the problem of regularity and uniqueness of martingale solutions, existence of weak solutions to stochastic geometric wave equations in the energy space and large-time behaviour of solutions. 2. The study of properties of stochastic convolutions driven by right-continuous martingales or Lévy processes and by Gaussian processes that are not semimartingales (typically, the fractional Brownian motion) in Hilbert and Banach spaces. 3. Infinite dimensional stochastic control and the associated semilinear Hamilton-Jacobi-Bellman equations in infinite dimensions, in particular ergodic and adaptive control problems, including the corresponding ergodicity and uniform ergodicity problems for stochastic partial differential equations. 4. The study of properties of the Brownian net and related measure-valued processes, including the properties of the corresponding heat equations.