Магистратура
2022/2023
Модулярные формы Якоби: 30 лет спустя
Статус:
Курс по выбору (Математика)
Направление:
01.04.01. Математика
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1-й курс, 4 модуль
Формат изучения:
с онлайн-курсом
Онлайн-часы:
56
Охват аудитории:
для своего кампуса
Прогр. обучения:
Математика
Язык:
английский
Кредиты:
3
Контактные часы:
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