The Analysis, Arithmetic, Geometry course is one of the 2nd year Master of the Master's track Mathematics and Applications at [Université Paris-Saclay] (https://www.universite-paris-saclay.fr/en). The main aim of the course is to prepare students for a thesis in fundamental mathematics.
Our master's program M2 offers three crash courses (in differential geometry, algebra and complex analysis) in September, several fundamental advanced courses in the first term (such as algebraic geometry, number theory, ergodic theory and dynamical systems, groups and geometry; the subjects may vary slightly from year to year) and a number of more specialized courses in the second term (the subjects change regularly and completely, we try to be sufficiently diverse in our offer). Of course you are also expected to write and defend a master thesis under the guidance of a senior researcher. This can be done at Orsay mathematical department but also at another research unit if necessary.
Information
Skills
Master and apply cutting edge mathematical tools and methods.
Objectives
The main aim of the ''Analysis, Arithmetic, Geometry'' (AAG) course is to prepare students for a thesis in fundamental mathematics.
Career Opportunities
Career prospects
After a Master's or Master's + PhD: researcher or lecturer
Further Study Opportunities
PhD
Students with a 2nd year Master's degree have the possibility to pursue doctoral research.
Admission Route
Capacity
Available Places
Target Audience and Entry Requirements
M1 in fundamental mathematics or an equivalent level of qualification. Admission upon competitive exam.
Application Period(s)
From 01/03/2026 to 30/06/2026
Supporting documents
Compulsory supporting documents
Motivation letter.
All transcripts of the years / semesters validated since the high school diploma at the date of application.
Curriculum Vitae.
Additional supporting documents
Document at your convenience.
Detailed description and hourly volume of courses taken since the beginning of the university program.
VAP file (obligatory for all persons requesting a valuation of the assets to enter the diploma).
Recommendation letters.
Document indicating the list of local M2 choices available here : https://urlz.fr/i3Lo.
Supporting documents :
- Residence permit stating the country of residence of the first country
- Or receipt of request stating the country of first asylum
- Or document from the UNHCR granting refugee status
- Or receipt of refugee status request delivered in France
- Or residence permit stating the refugee status delivered in France
- Or document stating subsidiary protection in France or abroad
- Or document stating temporary protection in France or abroad.
Details of the UEs taken for candidates outside the M1 Paris Saclay.
| Subjects | ECTS | Semester | Lecture | directed study | practical class | Lecture/directed study | Lecture/practical class | directed study/practical class | distance-learning course | Project | Supervised studies |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Groups and Geometries 2025-2026 | 15 | Semester 1 | 50 | 25 | |||||||
| Representation theory 2025-2026 | 7.5 | Semester 1 | 25 | 12.5 | |||||||
| Introduction to complex manifolds and Riemann surfaces 2025-2026 | 15 | Semester 1 | 50 | 25 | |||||||
| Homological Algebra 2025-2026 | 7.5 | Semester 1 | 25 | ||||||||
| Ergodic Theory 2025-2026 | 7.5 | Semester 1 | 25 | 12.5 | |||||||
| Global Analysis and Diffusion 2025-2026 | 7.5 | Semester 1 | 25 | 12.5 | |||||||
| Topological and Differentiable Dynamical Systems 2025-2026 | 7.5 | Semester 1 | 25 | 12.5 | |||||||
| Number Theory 2025-2026 | 15 | Semester 1 | 50 | 25 | |||||||
| Algebraic geometry : Scheme Theory 2025-2026 | 15 | Semestre 1 | 50 | 25 | |||||||
| Subjects | ECTS | Semester | Lecture | directed study | practical class | Lecture/directed study | Lecture/practical class | directed study/practical class | distance-learning course | Project | Supervised studies |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Topics in Commutative Algebra, Homological Algebra and Sheaves Theory 2025-2026 | 3 | Semester 2 | 22 | ||||||||
| Topics in Functional Analysis 2025-2026 | 3 | Semester 2 | 21 | ||||||||
| Topics in Differential Geometry 2025-2026 | 3 | Semester 2 | 21 | ||||||||
| Anglais/FLE | 3 | Semestre 2 | 24 | ||||||||
| A2 - Séminaire Etudiant | 3 | Semestre 2 | |||||||||
| Subjects | ECTS | Semester | Lecture | directed study | practical class | Lecture/directed study | Lecture/practical class | directed study/practical class | distance-learning course | Project | Supervised studies |
|---|---|---|---|---|---|---|---|---|---|---|---|
| AAG - Mémoire | 21 | Semestre 2 | |||||||||
| Subjects | ECTS | Semester | Lecture | directed study | practical class | Lecture/directed study | Lecture/practical class | directed study/practical class | distance-learning course | Project | Supervised studies |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Asymptotic problems in complex analysis 2025-2026 | 6 | Semester 2 | 20 | ||||||||
| Algorithms in number theory 2025-2026 | 6 | Semester 2 | 20 | 10 | |||||||
| Topoi and condensed mathematics 2025-2026 | 6 | Semester 2 | 20 | ||||||||
| Cartan Connections and Homogeneous Complex Geometry 2025-2026 | 6 | Semester 2 | 20 | ||||||||
| Toric varieties 2025-2026 | 6 | Semester 2 | 20 | ||||||||
| Measured group theory 2025-2026 | 6 | Semester 2 | 20 | ||||||||
| Analytic methods in hyperbolic dynamical systems 2025-2026 | 6 | Semester 2 | 20 | ||||||||
Teaching Location(s)
Training campus
