Explore the fascinating world of nonrational toric geometry in this 53-minute minicourse on symplectic toric quasifolds. Delve into the historical development and core concepts of toric quasifolds, which generalize toric varieties to simple convex polytopes that are not rational. Examine key notions such as quasilattices, quasirationality, and quasitori through various examples, including quasispheres, Penrose tilings, quasicrystals, regular convex polyhedra, and irrational Hirzebruch surfaces. Learn about the generalized Delzant construction, symplectic reduction, and nonrational cuts. Gain insights from recent research findings presented by Dr. Elisa Prato from Universita Degli Studi Firenze, in collaboration with other experts in the field.