Banach space analysis and measure theory: Tensor products and operator ideals; geometry of Banach spaces; interplay between Banach space theory and measure theory. Operator algebras: Spectral, Riesz and Fredholm theory; noncommutative analysis on C*-dynamical systems, with emphasis on the recurrence properties of such systems, and applications to quantum statistical mechanics. Stochastic analysis and applications to the mathematics of finance. Theory of double families of evolution operators, their spectral theory and applications to dynamic boundary condition problems, the Navier-Stokes equations (existence and uniqueness results) and problems in nonlinear elasticity theory