Number theory II.b - Modular forms

MATH-511 / 5 credits

Teacher: Viazovska Maryna

Language: English

Summary

In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.

Content

During the course we will learn:

  • Basic definitions and facts of the theory of modular forms
  • Combinatorial properties of the Fourier expansions of modular forms
  • Applications of modular forms to harmonic analysis
  • Modular forms and the sphere packing problem

 

Keywords

Modular forms, Modular group, linear frantional transformations, theta functions.

Learning Prerequisites

Required courses

 

 

 

Recommended courses

Required courses

Complex analysis

Fourier analysis

Recommended courses

Algebraic topology

Riemann surfaces.

 

Assessment methods

Weekly graded homeworks and oral exam

Resources

Bibliography

Bibliography

 

  1. A first course in modular forms. Fred Diamond; Jerry Shurman; 2005
  2. The 1-2-3 of modular forms : lectures at a summer school in Nordfjordeid, Norway. Don Zagier; 2008
  3. Topics in Classical Automorphis forms. Henryc Iwaniec

 

 

Ressources en bibliothèque

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Number theory II.b - Modular forms
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Number theory II.b - Modular forms
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Number theory II.b - Modular forms
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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