Title of the course: Introduction to Modular Forms
Instructor: Dr. Davide Cesare Veniani
Institution: Universität Stuttgart
Dates: 25-30 July 2022
Prerequisites: The general topology, group theory and complex analysis usually covered in advanced undergraduate or first-year graduate courses.
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: In this course, I will introduce the basic notions of the theory of modular forms and explain its connections to the theory of Riemann surfaces, keeping the level as elementary as possible. Towards the end, I will review the role of modular forms in Viazovska’s solution of the sphere packing problem in dimension 8 and 24. This course will be a complement to Dino Festi’s course on Elliptic Curves.
Language: EN
Textbooks: J. S. Milne, Modular Functions and Modular Forms (https://www.jmilne.org/math/CourseNotes/mf.html); G. Wiese, Vorlesung über Modulformen (https://math.uni.lu/wiese/notes/MF.pdf); F. Diamond, J. Shurman. A first course in modular forms. Graduate Text in Mathematics, 228. Springer-Verlag, 2005