About this Course
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Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Advanced Level

Approx. 54 hours to complete

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

English

Subtitles: English
User
Learners taking this Course are
  • Data Scientists
  • Researchers
  • Teachers
  • Engineers
  • Software Engineers
User
Learners taking this Course are
  • Data Scientists
  • Researchers
  • Teachers
  • Engineers
  • Software Engineers

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Advanced Level

Approx. 54 hours to complete

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

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
1 hour to complete

Introduction to the Course

1 video (Total 14 min), 4 readings
1 video
4 readings
Course Overview10m
Grading and Logistics10m
Suggested Readings10m
About the Instructor10m
3 hours to complete

Jacobi modular forms: motivations

5 videos (Total 62 min), 1 quiz
5 videos
Theta-function12m
Modular and abelian transformations12m
Pullbacks of theta-function12m
Modular forms12m
Week
2
3 hours to complete

Jacobi modular forms: the first definition

6 videos (Total 75 min), 1 quiz
6 videos
Definition of Jacobi forms (part 2)13m
Basic properties of Jacobi forms12m
Jacobi modular group11m
Symplectic group11m
Jacobi modular group (part 2)13m
Week
3
3 hours to complete

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

6 videos (Total 86 min), 1 quiz
6 videos
The action of Jacobi modular group14m
The action of Jacobi modular group (part 2)10m
The second definition of Jacobi forms15m
Special values of Jacobi forms11m
The first theorem20m
Week
4
3 hours to complete

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

6 videos (Total 76 min), 1 quiz
6 videos
The zeros of Jacobi forms (part 2)11m
Taylor expansion of Jacobi forms12m
Taylor expansion of Jacobi forms (part 2)13m
Dimensions of some spaces of Jacobi forms10m
Examples of Jacobi modular forms14m

Instructor

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Valery Gritsenko

Laboratory of Algebraic Geometry and its Applications

About National Research University Higher School of Economics

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...

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

More questions? Visit the Learner Help Center.