Number theory II.a - Modular forms
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
- Basic definitions and facts of the theory of modular forms
- Combinatorial properties of the Fourier expansions of modular forms
- Modular forms and harmonic analysis
- Modular forms and the sphere packing problem
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
- A first course in modular forms Fred Diamond; Jerry Shurman; 2005
- 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
Mo | Tu | We | Th | Fr | |
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 |
Légendes:
Lecture
Exercise, TP
Project, other