Functional analysis is the study of spaces of functions and, generally, of topological vector spaces and their associated structures via topological, analytical and geometric methods.
It is a far-reaching field which plays a fundamental role in various areas including partial differential equations, function theory, complex analysis, harmonic analysis and topological group theory, mathematical physics, differential geometry, probability and measure theory.
Our main focus is on Banach spaces and Banach algebra. The geometry of Banach spaces is very rich with many intriguing examples of challenging spaces from areas as diverse as dynamics and logic. Banach algebra is involved in our research on noncommutative geometry (see below) and noncommutative complex analysis.