Об этом курсе
Недавно просмотрено: 2,062

100% онлайн

Начните сейчас и учитесь по собственному графику.

Гибкие сроки

Назначьте сроки сдачи в соответствии со своим графиком.

Продвинутый уровень

Прибл. 54 часа на выполнение

Предполагаемая нагрузка: 12 weeks of study, 3-5 hours per week...

Английский

Субтитры: Английский

100% онлайн

Начните сейчас и учитесь по собственному графику.

Гибкие сроки

Назначьте сроки сдачи в соответствии со своим графиком.

Продвинутый уровень

Прибл. 54 часа на выполнение

Предполагаемая нагрузка: 12 weeks of study, 3-5 hours per week...

Английский

Субтитры: Английский

Программа курса: что вы изучите

Неделя
1
1 ч. на завершение

Introduction to the Course

Welcome to the course! I hope you have an opportunity to reserve some time to explore the course content, course logic and our grading policy. The course consists of 12 lectures. This course will help you to start your progress in the field of the theory of Jacobi modular forms. Best regards, Valery Gritsenko

...
1 видео ((всего 14 мин.)), 4 материалов для самостоятельного изучения
1 видео
4 материала для самостоятельного изучения
Course Overview10мин
Grading and Logistics10мин
Suggested Readings10мин
About the Instructor10мин
3 ч. на завершение

Jacobi modular forms: motivations

This module is devoted to motivations to study Jacobi forms. We provide some first examples including theta-functions. Also there is a peer review in the end of this module.

...
5 видео ((всего 62 мин.)), 1 тест
5 видео
Motivations12мин
Theta-function12мин
Modular and abelian transformations12мин
Pullbacks of theta-function12мин
Modular forms12мин
Неделя
2
3 ч. на завершение

Jacobi modular forms: the first definition

This module is devoted to the first definition of Jacobi forms. In this module we also define Jacobi modular group. Also there is a peer review in the end of this module.

...
6 видео ((всего 75 мин.)), 1 тест
6 видео
Definition of Jacobi forms (part 2)13мин
Basic properties of Jacobi forms12мин
Jacobi modular group11мин
Symplectic group11мин
Jacobi modular group (part 2)13мин
Неделя
3
3 ч. на завершение

Jacobi modular group and the second definition of Jacobi forms. Special values of Jacobi modular forms

This module is devoted to the second definition of Jacobi forms. In this module we also consider special values of Jacobi forms. Also there is a peer review in the end of this module.

...
6 видео ((всего 86 мин.)), 1 тест
6 видео
The action of Jacobi modular group14мин
The action of Jacobi modular group (part 2)10мин
The second definition of Jacobi forms15мин
Special values of Jacobi forms11мин
The first theorem20мин
Неделя
4
3 ч. на завершение

Zeros of Jacobi forms. The Jacobi theta-series, the Dedekind eta-function and the first examples of Jacobi modular forms

This module is devoted to zeros of Jacobi modular forms, their Taylor extensions and the first examples of Jacobi forms. Using classical Jacobi theta-series and Dedekind eta-function we construct a series of Jacobi forms. Also there is a peer review in the end of this module.

...
6 видео ((всего 76 мин.)), 1 тест
6 видео
The zeros of Jacobi forms (part 2)11мин
Taylor expansion of Jacobi forms12мин
Taylor expansion of Jacobi forms (part 2)13мин
Dimensions of some spaces of Jacobi forms10мин
Examples of Jacobi modular forms14мин
Неделя
5
3 ч. на завершение

The Jacobi theta-series as Jacobi modular form. The basic Jacobi modular forms

This module is devoted to detailed study of Jacobi theta-series. We will discuss abelian, modular and some other properties of this function. Also there is a peer review in the end of this module.

...
6 видео ((всего 84 мин.)), 1 тест
6 видео
Properties of Jacobi theta-function9мин
Properties of Jacobi theta-function (part 2)13мин
Properties of Jacobi theta-function (part 3)15мин
Construction of Jacobi forms using theta-series15мин
Construction of Jacobi forms using theta-series (part 2)13мин
Неделя
6
4 ч. на завершение

Theta-blocks, theta-quarks and the first Jacobi cusp form of weight 2

This module is devoted to very important notion of theta-blocks and theta-quarks. In this module we also construct the first Jacobi form of weight 2. Also there is a peer review in the end of this module.

...
7 видео ((всего 96 мин.)), 1 тест
7 видео
Theta-blocks14мин
Theta-blocks (part 2)13мин
Theta-quarks14мин
Dimension of the space of Jacobi forms of odd weight14мин
Theta-quarks (part 2)11мин
The proof of theorem about theta-quarks16мин
The first Jacobi cusp form of weight 210мин
Неделя
7
4 ч. на завершение

Jacobi forms in many variables and the Eichler-Zagier Jacobi forms

This module is devoted to Jacobi forms in many variables. In this module we also define classical Eichler-Zagier Jacobi forms in terms of Jacobi forms in many variables. Also there is a peer review in the end of this module.

...
6 видео ((всего 93 мин.)), 1 тест
6 видео
Jacobi theta-series and Jacobi forms in many variables (part 2)15мин
Hyperbolic reformulation14мин
Examples of Jacobi forms in many variables14мин
Examples of Jacobi forms in many variables (part 2)16мин
Examples of Jacobi forms in many variables (part 3)16мин
Неделя
8
3 ч. на завершение

Jacobi forms in many variables and the splitting principle. Theta-quarks as a pull-back. Weak Jacobi forms in many variables

In this module we continue studying Jacobi forms in many variables. Among other things we discuss splitting principle and realize theta-quarks as a pull-back. Also there is a peer review in the end of this module.

...
6 видео ((всего 90 мин.)), 1 тест
6 видео
Theta-quarks as pull-backs of Jacobi forms (part 2)16мин
Theta-quarks as pull-backs of Jacobi forms (part 3)13мин
The splitting principle15мин
The splitting principle (part 2)16мин
Weak Jacobi forms in many variables13мин
Неделя
9
3 ч. на завершение

The Weil representation and vector valued modular forms. Jacobi forms of singular weight

This module is devoted to very useful notion of the Weil representation and vector-valued modular forms. In this module we also define Jacobi forms of singular weight. Also there is a peer review in the end of this module.

...
6 видео ((всего 85 мин.)), 1 тест
6 видео
The Weil representation (part 2)15мин
Jacobi forms of singular weight14мин
Jacobi forms of singular weight (part 2)15мин
Jacobi forms of critical weight15мин
Jacobi forms of critical weight (part 2)12мин
Неделя
10
3 ч. на завершение

Quasi-modular Eisenstein series. The automorphic correction of Jacobi forms and Taylor expansions

This module is devoted to Quasi-modular Eisenstein series. In this module we also define the automorpic correction of Jacobi forms and its Taylor expansion that gives us the way to construct the series of Jacobi forms. Also there is a peer review in the end of this module.

...
6 видео ((всего 84 мин.)), 1 тест
6 видео
Differential operator D15мин
Quasi-modular Eisenstein series15мин
Automorphic correction and Taylor expansions13мин
Automorphic correction of Jacobi forms in many variables12мин
Automorphic correction of Jacobi forms in many variables (part 2)12мин
Неделя
11
3 ч. на завершение

Modular differential operators. The graded ring of the weak Jacobi modular forms

This module is devoted to Modular differential operators. In this module we also consider the Jacobi forms as the space with the structure of the bigraded ring. Also there is a peer review in the end of this module.

...
6 видео ((всего 90 мин.)), 1 тест
6 видео
Heat operator14мин
Heat operator (part 2)15мин
Applications of differential operators for Jacobi forms11мин
The graded ring of the weak Jacobi modular forms17мин
Jacobi type forms in many variables14мин
Неделя
12
3 ч. на завершение

Jacobi type forms and the generalisation of the Cohen-Kuznetsov-Zagier operator

The last module is devoted to Jacobi type forms. In this module we also consider the generalisation of the Cohen-Kuznetsov-Zagier operator. Also there is a peer review in the end of this module.

...
4 видео ((всего 52 мин.)), 1 тест
4 видео
A new proof of Cohen-Kuznetsov-Zagier theorem13мин
A new proof of Cohen-Kuznetsov-Zagier theorem (part 2)9мин
Cohen-Kuznetsov-Zagier theorem in case of many variables14мин

Преподаватели

Avatar

Valery Gritsenko

Laboratory of Algebraic Geometry and its Applications

О Национальный исследовательский университет "Высшая школа экономики"

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

Часто задаваемые вопросы

  • Зарегистрировавшись на сертификацию, вы получите доступ ко всем видео, тестам и заданиям по программированию (если они предусмотрены). Задания по взаимной оценке сокурсниками можно сдавать и проверять только после начала сессии. Если вы проходите курс без оплаты, некоторые задания могут быть недоступны.

  • Оплатив сертификацию, вы получите доступ ко всем материалам курса, включая оцениваемые задания. После успешного прохождения курса на странице ваших достижений появится электронный сертификат. Оттуда его можно распечатать или прикрепить к профилю LinkedIn. Просто ознакомиться с содержанием курса можно бесплатно.

Остались вопросы? Посетите Центр поддержки учащихся.