The group performs research in the fields of stocastich calculus, stochastic differential equations (SDEs), and stochastic partial differential equations (SPDEs), of diffusive type and, possibly, with jumps. More precisely, the group studies the following subjects: linear and non-linear Kolmogorov-Fokker-Planck equations; degenerate diffusions and ultra-parabolic differential operators; density estimates for diffusive stochastic processes, possibly in the presence of jumps, under weak Hörmander conditions; mean field stochastic differential equations and corresponding Kolmogorov equations; backward stochastic differential equations (BSDEs) and non-linear Feynman-Kac formulae for elliptic or parabolic non-linear partial differential equations; numerical methods of probabilistic type and analytic approximation; applications to Mathematical Finance and Engineering.