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

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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

• A first course in modular forms Fred Diamond / Jerry Shurman

Moodle Link

• https://go.epfl.ch/MATH-511