In this talk, we introduce positive quasimodular forms and study their basic properties. As applications, we provide algebraic proofs of quasimodular form inequalities that appear in the works of Viazovska and Cohn–Kumar–Miller–Radchenko–Viazovska on the resolution of optimal 8- and 24-dimensional sphere packing and universal optimality. We also present new upper bounds for the Bourgain–Clozel–Kahane sign uncertainty principle.