Sampling, Tilings, and Quasicrystals

Explore the connections between classical sampling theory and tiling properties in this Math Associates Seminar lecture. Delve into the Fuglede's theorem and conjecture, examining their relationship to Paley Wiener spaces. Investigate the role of model sets in sampling problems, originally introduced by Meyer for studying algebraic character approximations in locally compact abelian groups. Learn how model sets became crucial in describing diffraction patterns of quasicrystals following Shechtman's groundbreaking discovery in the 1980s. Gain insights from speaker Jorge Antezana of Universidad Nacional De La Plata in this comprehensive exploration of sampling, tilings, and quasicrystals.