From crystal to quasicrystal

This talk explores the mathematical structures underlying crystals and quasicrystals, tracing the evolution from periodic to aperiodic order. We will discuss how classical crystallography gives way to more general symmetry concepts in the study of quasicrystals, highlighting their discovery, mathematical models, and surprising regularities. Along the way, we’ll examine how these structures challenge traditional notions of symmetry and order, with insights from group theory, tiling theory, and a touch of geometry.