Modular forms and their applications to sphere packing and energy minimization

This minicourse will give an introduction to the theory of modular forms with a view towards applications to the sphere packing and energy minimization problems. In addition to some classical topics such as the theory of theta functions of lattices, I will also cover quasi-modular forms and modular integrals and explain how these arise in the work of Viazovska on sphere packing and in the work of Cohn-Kumar-Miller-Radchenko-Viazovska on energy minimization in dimensions 8 and 24.