MATH-417 / 5 crédits

Enseignant:

Langue: Anglais

Remark: pas donné en 2020-21


Summary

This year's topic is "Adelic Number Theory" or how the language of adeles and ideles and harmonic analysis on the corresponding spaces can be used to revisit classical questions in algebraic number theory

Content

Learning Prerequisites

Required courses

Anbalysis III & IV

Galois Theory.

Rings and Modules.

Introduction to Algebraic Number Theory.

 

Recommended courses

Not required but possibly useful

Introduction to Analytic Number Theory.

It will be good to have had some exposure to the theory of Riemann's zeta function.

Automorphic forms and L-functions.

Some exposure to the classical theory of modular forms migh be used at the end of the course to compare with the adelic viewpoint.

 

Important concepts to start the course

-Good knowledge of Galois theory, Algebraic Number Theory and the associated commutative algebra.

Learning Outcomes

By the end of the course, the student must be able to:

  • Synthesize the theory of adeles and ideles
  • Solve basic problems involving adeles and ideles
  • Interpret classical problems in the adelic language

Transversal skills

  • Access and evaluate appropriate sources of information.
  • Make an oral presentation.
  • Demonstrate the capacity for critical thinking

Teaching methods

Ex-Cathedra Course

Expected student activities

We expect a proactive attitude during the courses and the exercises sessions (possibly with individual presentation of the solution of various problems).

Assessment methods

Exam Oral

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.

Supervision

Office hours No
Assistants Yes
Forum No
Others a moodle with ressources for the course will be maintained

Prerequisite for

Current research in number theory

Dans les plans d'études

  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Topics in number theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Topics in number theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Topics in number theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Oral (session d'hiver)
  • Matière examinée: Topics in number theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
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