Master 2 in Fundamental Mathematics

The 2nd year of our Master pathway in Fundamental Mathematics prepares students to undertake research in mathematics, either pure or applied.

  1. General organization
  2. Lectures
  3. Seminar and internship
  4. Advanced lectures
  5. Scientific events

General organization

The curriculum provides Master students with a large variety of lectures and scientific events, partly renewed every year. It mixes items contributing to the student grades (lectures, seminar, internship) with elements less formal but fostering students insertion into research activities (advanced lectures, master classes,...).

The program takes place in Rennes but receives contributions from all institutions and universities of Rennes and Brest.

It also benefits from the support of the Henri Lebesgue Center, promoting excellence of research in mathematics in our regional area. In particular the Henri Lebesgue Center provides Master scholarships for talented students  https://www.lebesgue.fr/content/bourses_master .

It takes part to the French-Vietnamese Master program in applied maths.

Students may apply to the 2nd year of our Master program directly through https://candidatures.univ-rennes1.fr , or for foreigner students through https://pastel.diplomatie.gouv.fr/etudesenfrance .

Lectures

Partly renewed each year, our lectures typically cover a broad range of mathematics, either pure or applied: algebra, algebraic geometry, analysis, arithmetics, cryptography, differential geometry, dynamical systems, ergodic theory, numerical analysis, partial differential equations, probability, spectral theory, statistics, stochastic calculus, topology.
 

Though lectures are organized by thematics, students may mix lectures from different thematics. Likewise, though only four of them are required at first semester, and two only at second semester, students may attend more lectures at both semesters.

To a large extent, our schedule is synchronized (and travel expenses taken in charge by the Henri Lebesgue Center) to provide students with the opportunity to also attend lectures in a partner Master program in Nantes. At the begining of each semester lectures of both programs are presented jointly.

Lectures are given in English unless only French-speaking students are attending them.

Seminar and internship

Along the first semester, students read a research paper that they present to other students of their thematic during a series of student talks, called "seminar". Their preparation is supervised by a mathematician of Rennes and thus it also fosters students meeting with potential internship advisors.

The year ends with an internship, at least two-months long, in a mathematical research department. During the internship, students prepare a Master thesis. Preferably, for students aiming at an academic career, the internship is a preparation to topics of the planned Ph.D. thesis under the supervision of a prospective Ph.D. advisor.

Part of the first semester of each student is devoted to the identification of a topic and an advisor for the Master internship, suiting its mathematical tastes. During this process, students are guided by the chair of the program, those of  thematics, lecturers or seminar advisors. They make the most of local --- in particular within the Henri Lebesgue Center ---, national and international networks of mathematical departments of Rennes, IRMAR --- a highly-ranked department with international recognition --- and Rennes' branch of CREST, and of Brest, LMBA.

Advanced lectures

The curriculum also includes more advanced lectures that do not contribute to Master grades.
 

https://irmar.univ-rennes1.fr/cours-doctoraux-lirmar

By definition, doctoral lectures are principally designed for Ph.D. students. However, since they take place at second semester, when Master students have acquired necessary background, they are largely open to Master students.

Four to eight-hours long, they are focused on an advanced specific topic. Topics and schedules are coordinated with those of the Master program.

As for 2018-2019 propositions include

  • "Algebraic geometry and analytic geometry" by Serge Cantat
  • "Dispersive equations" by Rémi Carles
  • "Mathematical statistical mechanics" by Mathias Rousset
http://journees-louis-antoine.univ-rennes1.fr/

Days Louis Antoine is a series of Masterclasses taking place twice a year in Rennes.

Each session brings in Rennes for two days two experts at the forefront of a contemporary research topic and well-known for their expository skills. Each of them gives a four-hours series of lectures, starting at Master level and bringing students at the edge of their field.

As for 2018-2019, are planned

  • "Computer-assisted proofs", by Bruno Salvy and Assia Mahboubi, on the 22nd and 23th of November 2018
  • "Magnetization and percolation", by Christophe Garban and Hugo Duminil-Copin, on the 31st of January and the 1st of February 2019
https://www.lebesgue.fr/fr//content/master_classes

Taking place in Angers on three days of December, Master classes of Angers are principally designed for Master students from Rennes and Nantes. They provide in parallel two series of lectures on two distinct topics.
 

Scientific events

Organized by IRMAR or one of its partners within the Henri Lebesgue Center, some scientific events are largely open to Master students.
 

https://irmar.univ-rennes1.fr/seminaire-gaussbusters
https://irmar.univ-rennes1.fr/seminaire-landau
https://irmar.univ-rennes1.fr/seminaire-pampers
http://www.ensai.fr/recherche/seminaires/les-seminaires-de-statistique-d...

Held all along the year by Ph.D. students from Rennes, thematic-wise, seminars of young researchers provide a view on current researchs through talks by Ph.D. students.

Being rather informal, thoses seminars foster Master students' discussions with Ph.D. students of their thematic.

https://www.lebesgue.fr/fr/content/rencontres_doctorales

As a natural continuation of young researchers seminars, but on the area of the Henri Lebesgue Center, doctoral meetings Lebesgue is a yearly series of conferences, grouping together all thematics.

https://www.lebesgue.fr/5min
https://www.youtube.com/playlist?list=PLZ5ZEffH1cUAkodxGDs0SNif_wScXNTU0

"5 minutes Lebesgue" is a series of mathematical videos, consisting in 5 minutes talks by a mathematician from the Centre Henri Lebesgue or one of its guests.

Presentations from Rennes are videotaped live each Tuesday at 3h45pm, and followed by a small refreshment. For Master students this offers an informal opportunity to meet with researchers from Rennes.

https://www.lebesgue.fr/content/semestres

Each year the Henri Lebesgue Centre Henri organizes a series of conferences on a specific mathematical field. Among those conferences schools initiate young researchers to a specific topic.

Traditionally they are held at spring or summer at a time when Master students have acquired necessary background to attend them.

As for 2019, see
https://www.lebesgue.fr/content/sem2019-groups
https://www.lebesgue.fr/content/sem2019-perfectoids