Fourier Quasicrystals from Stable Polynomials
Explore the construction of one-dimensional Fourier quasicrystals through the lens of multivariate stable polynomials, delving into the rich interplay between algebra and harmonic analysis.
Cynthia Vinzant (University of Washington)
Beyond Graph Laplacians
A Fourier quasicrystal is a discrete subset of Euclidean space whose Fourier transform is also discrete. These sets are almost periodic, often without being periodic or even containing long arithmetic progressions. In 2020, Kurasov and Sarnak gave a method for constructing one-dimensional Fourier quasicrystals from multivariate stable polynomials, which are polynomials whose zeroes avoid certain regions in the complex plane. The rich theory of stable polynomials can be used to control and extract features of the corresponding quasicrystals. Analogous varieties of higher codimension also give rise to higher dimensional quasicrystals. I will give an introduction to these objects and the beautiful connection between them.