Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties

Explore a comprehensive lecture on Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties presented by Pavel Kurasov from Stockholm University. Delve into the analysis and mathematical physics of Fourier Quasicrystals (FQ), beginning with their definition as crystalline measures. Examine the connection between one-dimensional FQs with positive integer weights and stable Lee-Yang polynomials. Investigate multidimensional Fourier quasicrystals and learn how a general family of FQs in ℝd with positive integer weights can be constructed using co-dimension d Lee-Yang varieties in ℂn. Understand the properties of these complex algebraic varieties and their relation to Lee-Yang polynomial zero sets. Discover how these FQs can be supported by Delaunay almost periodic sets and their genuinely multidimensional nature. Compare this approach to recent work by Yves Meyer, Lawton-Tsikh, and de Courcy-Ireland-K. Contemplate whether this construction encompasses all multidimensional FQs with positive integer masses. Gain insights from this joint work with L. Alon, M. Kummer, and C. Vinzant, as presented at the Institute for Advanced Study.

Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties - Pavel Kurasov