Cohomological invariants and perturbation problems for Fourier algebras and group algebras

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My main field of research straddles the boundary of several domains within mathematics: functional analysis, harmonic analysis, and abstract algebra. Let me try to give an overview of what some of these terms mean. Functional analysis is a branch of mathematics which originated in the early 20th century, motivated by the need to formulate and study systems of differential equations that model various physical phenomena. It has historically had close links with the branch of mathematics known as Fourier analysis, which is an ancestor of harmonic analysis, and is concerned with the study of periodic motion or signals, such as vibration in a string or an air column, or electro-magnetic waves.