2023/2024

Jacobi modular forms: 30 ans apres

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 4 module

Online hours: 56

Open to: students of one campus

Instructors: Valery Gritsenko

Language: English

ECTS credits: 3

Contact hours: 6

Course Syllabus

Abstract

Jacobi forms are holomorphic functions in two complex variables. They are modular in one variable and abelian (or double periodic) in another variable. The theory of Jacobi modular forms became an independent research subject after the famous book of Martin Eichler and Don Zagier “Jacobi modular forms” (Progress in Mathematics, vol. 55, 1985) which was cited more than a thousand times in research papers. This is due to many applications of Jacobi forms in arithmetic, topology, algebraic and differential geometry, mathematical and theoretical physics, in the theory of Lie algebras, etc. The main hero of the course is the Jacobi theta-series. Using it we will construct a lot of concrete examples of Jacobi forms in one or many abelian variables, in particular, Jacobi forms for root systems