Selected Topics in Analysis: Stochastic PDEs with applications to climate sciences

The course will cover the following key areas: Stochastic differential equations (basic notions, invariant measures and long time behaviour, connection between SDEs and PDEs), stochastic equations in infinite dimensions (random variables in infinite dimensions, gaussian measures, Wiener processes, SPDEs with additive noise with Lipschitz and locally Lipschitz non-linearities), energy balance climate models (introduction, derivation, mathematical analysis, and numerical simulations (if time allows)). Further information can be found at https://drive.google.com/file/d/1ZCBUtwbkAaUzJpYqqEK_bsydMRh5KgTF/view?usp=sharing