The area of research within Pure Mathematics Dr Mathieu has been involved in over the last number of years can be most adequately described as Noncommutative Functional Analysis.

Traditional Functional Analysis, as it was formed by Stefan Banach early in the 20th century on the basis of the work of many others, seeks to understand Banach spaces and operators between them. Noncommutative Functional Analysis grew out of the theory of C* -algebras, which are algebras of bounded linear operators on Hilbert space.

The new structure arises by enriching a Banach space with a 'noncommutative' structure allowing an embedding into a space of operators on Hilbert space. Being a subspace of an algebra whose multiplication is in general noncommutative, many new features appear for an operator space which are invisible or non-existent at the Banach space level.