Function algebras and operator algebras arising in noncommutative harmonic analysis

Noncommutative generalizations of the classical Fourier transform give rise to algebraic objects whose structural properties can be studied using methods from functional analysis. Key examples include Fourier algebras (algebras of functions) and group C*-algebras (algebras of operators). The main part of the project will investigate homological invariants, such as spaces of derivations and cocycles, of Fourier algebras and their relatives. Links to operator spaces and operator systems will be explored, as will potential generalizations to L^p-settings.