Homological invariants of Fourier algebras (24rit022)

The Banff International Research Station will host the "Homological invariants of Fourier algebras" Research in Teams workshop in Banff from March 3 - 10 , 2024.

Harmonic analysis and functional analysis are two closely related areas of mathematics, which evolved from tools developed to analyze differential equations arising in physics and chemistry, and have since found further applications in number theory, signal processing and quantum mechanics. Fourier algebras of locally compact groups sit at the interface between these two areas; they are normed algebras of functions that encode both the topological and the algebraic structure of the original groups.

This Research In Teams will investigate certain numerical and algebraic invariants of Fourier algebras, building on recent progress by the team members that made use of their complementary expertise. Such invariants have been much studied for other classes of Banach algebras, such as semigroup algebras or $C^{\ast}$-algebras, but much less has been done for Fourier algebras; this project aims to develop new tools for calculating these invariants and hence deepen our understanding of Fourier algebras.