Number theory II.a - 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

Learning Prerequisites

Required courses

Complex analysis, harmonic analysis, discrete mathematics, a basic course in topology.

Recommended courses

Riemann surfaces, Riemannian manifolds, Lie groups, analytic number theory.

Assessment methods

70% of the final grade are awarded for the final exam and 30% of the grade come from the homework done during the semester.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Resources

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, [June 2004]

Ressources en bibliothèque

Moodle Link

In the programs

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

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22