Banach space analysis and measure theory

The following topics are covered: 
Tensor products and operator ideals
Geometry of Banach spaces
Interplay between Banach space theory and measure theory
Amenability of Banach Algebra

Operator algebras

The focus is on noncommutative analysis on C*-dynamical systems, with emphasis on the recurrence properties of such systems, and applications to quantum statistical mechanics.

Fixed point theory and its applications

Approximation theory and orthogonal polynomials

Stochastic analysis and applications to the mathematics of finance

Convergence spaces and applications to analysis, including applications to:

Riesz spaces and ordered topological vector spaces
Generalized functions and solutions of nonlinear PDEs

Theory of double families of evolution operators, their spectral theory and applications

    Applications are directed to:
Dynamic boundary condition problems
The Navier-Stokes equations (existence and uniqueness results)
Problems in nonlinear elasticity theory
Non-Newtonian fluid mechanics