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

英語

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100%オンライン

自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

上級レベル

約54時間で修了

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

英語

字幕:英語

シラバス - 本コースの学習内容

1
1時間で修了

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件のビデオ (合計14分), 4 readings
1件のビデオ
4件の学習用教材
Course Overview10 分
Grading and Logistics10 分
Suggested Readings10 分
About the Instructor10 分
3時間で修了

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件のビデオ (合計62分), 1 quiz
5件のビデオ
Theta-function12 分
Modular and abelian transformations12 分
Pullbacks of theta-function12 分
Modular forms12 分
2
3時間で修了

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件のビデオ (合計75分), 1 quiz
6件のビデオ
Definition of Jacobi forms (part 2)13 分
Basic properties of Jacobi forms12 分
Jacobi modular group11 分
Symplectic group11 分
Jacobi modular group (part 2)13 分
3
3時間で修了

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件のビデオ (合計86分), 1 quiz
6件のビデオ
The action of Jacobi modular group14 分
The action of Jacobi modular group (part 2)10 分
The second definition of Jacobi forms15 分
Special values of Jacobi forms11 分
The first theorem20 分
4
3時間で修了

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件のビデオ (合計76分), 1 quiz
6件のビデオ
The zeros of Jacobi forms (part 2)11 分
Taylor expansion of Jacobi forms12 分
Taylor expansion of Jacobi forms (part 2)13 分
Dimensions of some spaces of Jacobi forms10 分
Examples of Jacobi modular forms14 分
5
3時間で修了

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件のビデオ (合計84分), 1 quiz
6件のビデオ
Properties of Jacobi theta-function9 分
Properties of Jacobi theta-function (part 2)13 分
Properties of Jacobi theta-function (part 3)15 分
Construction of Jacobi forms using theta-series15 分
Construction of Jacobi forms using theta-series (part 2)13 分
6
4時間で修了

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件のビデオ (合計96分), 1 quiz
7件のビデオ
Theta-blocks (part 2)13 分
Theta-quarks14 分
Dimension of the space of Jacobi forms of odd weight14 分
Theta-quarks (part 2)11 分
The proof of theorem about theta-quarks16 分
The first Jacobi cusp form of weight 210 分
7
4時間で修了

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件のビデオ (合計93分), 1 quiz
6件のビデオ
Jacobi theta-series and Jacobi forms in many variables (part 2)15 分
Hyperbolic reformulation14 分
Examples of Jacobi forms in many variables14 分
Examples of Jacobi forms in many variables (part 2)16 分
Examples of Jacobi forms in many variables (part 3)16 分
8
3時間で修了

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件のビデオ (合計90分), 1 quiz
6件のビデオ
Theta-quarks as pull-backs of Jacobi forms (part 2)16 分
Theta-quarks as pull-backs of Jacobi forms (part 3)13 分
The splitting principle15 分
The splitting principle (part 2)16 分
Weak Jacobi forms in many variables13 分
9
3時間で修了

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件のビデオ (合計85分), 1 quiz
6件のビデオ
The Weil representation (part 2)15 分
Jacobi forms of singular weight14 分
Jacobi forms of singular weight (part 2)15 分
Jacobi forms of critical weight15 分
Jacobi forms of critical weight (part 2)12 分
10
3時間で修了

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件のビデオ (合計84分), 1 quiz
6件のビデオ
Differential operator D15 分
Quasi-modular Eisenstein series15 分
Automorphic correction and Taylor expansions13 分
Automorphic correction of Jacobi forms in many variables12 分
Automorphic correction of Jacobi forms in many variables (part 2)12 分
11
3時間で修了

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件のビデオ (合計90分), 1 quiz
6件のビデオ
Heat operator14 分
Heat operator (part 2)15 分
Applications of differential operators for Jacobi forms11 分
The graded ring of the weak Jacobi modular forms17 分
Jacobi type forms in many variables14 分
12
3時間で修了

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件のビデオ (合計52分), 1 quiz
4件のビデオ
A new proof of Cohen-Kuznetsov-Zagier theorem13 分
A new proof of Cohen-Kuznetsov-Zagier theorem (part 2)9 分
Cohen-Kuznetsov-Zagier theorem in case of many variables14 分

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Valery Gritsenko

Laboratory of Algebraic Geometry and its Applications

ロシア国立研究大学経済高等学院(National Research University Higher School of Economics)について

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...

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