Amenability constants of Fourier algebras of virtually abelian groups

by Yemon Choi (Lancaster University)

Monday 8 Jun 2026, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

In classical Fourier analysis on the circle, a fundamental object of study is the algebra of complex-valued functions on the circle whose Fourier series are absolutely summable. For any virtually abelian locally compact group G, one can make an analogous definition using the operator-valued Fourier transform; this is one way to define the Fourier algebra A(G). I will discuss a quantitative invariant associated to A(G), its so-called amenability constant, and present some results and conjectures on how this invariant behaves with respect to natural group-theoretic operations. There is an explicit formula for this invariant when G is finite, in terms of the degrees of irreducible characters of G, and if time permits I will present some partial results on the possible values that can be attained for finite groups.