Master
2022/2023
Jacobi modular forms: 30 ans apres
Type:
Elective course (Mathematics and Mathematical Physics)
Area of studies:
Mathematics
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1 year, 4 module
Mode of studies:
distance learning
Online hours:
56
Open to:
students of one campus
Master’s programme:
Mathematics and Mathematical Physics
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