Alternating cocycles on Beurling-Fourier algebras (26rit046)
Organizers
Yemon Choi (Lancaster University)
Mahya Ghandehari (University of Delaware)
Description
The Banff International Research Station will host the “Alternating cocycles on Beurling-Fourier algebras” Research in Teams program from January 4 - 11, 2026.
Harmonic analysis and functional analysis are two closely related areas of mathematics. They 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.
During the last 15 years, there has been renewed interest in weighted analogues of these objects, known as Beurling–Fourier algebras. Building on recent advances in our understanding, this Research In Teams will investigate certain cohomological invariants of these algebras. Such invariants were previously studied when the underlying group is commutative; this project aims to extend those results to to noncommutative Lie groups, by making use of the complementary expertise of the team members. Progress on this project will deepen our understanding of how Beurling–Fourier algebras resemble or differ from their unweighted versions.
The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta’s Advanced Education and Technology.