Admitted in Ecole Polytechnique

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400 Admitted in Ecole Polytechnique The 0.3
TOP Students
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The Ecole Polytechnique
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An outstanding campus
? 15 km away from Paris, 200 hectares
? 9000 m2 of sports facilities rugby, soccer,
riding, swimming, climbing, golf, fencing,
athletics
? 52 lecture halls and classrooms
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Ecole Polytechnique

The Master of Pure Mathematics
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M1 60 ECTS

• 1 course 9 weeks
• (1h30 theory 2h exercises/week)

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Semester 1 (Majeure 1) 25 ECTS

• 3 courses among the following (5 ECTS each)
• - Algebra, arithmetic and codes (Mestre, Paris
  VI)
• - Fluid mechanic (Gallagher, Paris VII)
• - Symmetric groups (Kosmann-Schwarzbach, École
  polytechnique)
• - Dynamical systems (Viterbo, École
  polytechnique)
• and
• -1 course of Foreign Languages (5 ECTS)

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? A research project (5 ECTS) whose subject is
related to one of the previous courses (from
September, 15 to the end of December)
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Semester 2 (Majeure 2) 35 ECTS

• 3 courses among the following (5 ECTS each)
• - Differential topology (Barge, École
  polytechnique)
• - Control theory (Gérard, Paris XI)
• - Elliptic curves (Bost, Paris XI)
• - General Relativity (Bourguignon, École
  polytechnique)

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? A deepening dissertation or research
internship (5 ECTS) whose subject is related to
one of the previous courses (from January, 15 to
the end of March)
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? The first Master Thesis or research internship
(15 ECTS), usually jointly with another
student. (from April, 15 to late June.)
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M2 60 ECTS

• Joined program with
• University Paris XI (Orsay)

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2 courses usually 4 x 12 hours during Semester
1 (15 ECTS each) with or without exercices (0
x 12, 2 x 12 or 4 x 12 hours) among
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On the Ecole Polytechnique Campus

• Introduction to Microlocal Analysis
• (BONY, Ecole Polytechnique)
• Homology
• (LANNES, Ecole Polytechnique)
• Introduction to Algebraic Geometry
• (LASZLO, Ecole Polytechnique)

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On the Orsay Campus

• Introduction to Riemann Surfaces (BOST, Paris
  XI)
• Introduction to Number Theory (CLOZEL, HENNIART,
  Paris XI)
• Introduction to Differential Geometry (PANSU,
  Paris XI)
• Introduction to dynamical system (GRACZYK, Paris
  XI)
• Harmonic analysis (AUSCHER, Paris XI)

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and also

• Spectral theory (SAUT, Paris XI)
• Evolution equations (BURQ, ZUILY, Paris XI)

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last but not least

• Main Master Thesis
• during the whole Semester 2
• 30 ECTS
• Study of some research article (no original
  results are required).

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One can apply for either the Engineer program
or to one Master degree pogram. Student in the
Engineer program can chose a Master degree
program if he passes, he will get both the
Diploma of Engineer of Ecole Polytechnique and
the corresponding Master degree.
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Fluid Structure interaction

• Recent emphasis on dynamics and coupling
• Interest on control and optimal design

Fluid structure in biomechanics
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Micromechanics what do you get ?
Plasticity of polycrystals (CFC, HC Zr, Ti,
Steels) from slip line (MEB-MET) to atomistic
?(ab initio) Cracks and microcracks (effects of
Fatigue, multiaxial loading, internal friction,
hydrogen) Microbucklings for fiber reinforced
materials Damage and rupture driving mechanisms
(fragile, ductile, precipites, anisotropy) Interf
acial physics (thin coatings gtµm, )
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Forthcoming challenge match macroscopic
approach and micromechanics.
Microstucture
Micromodeling
Key modeling issues
Real time reliable macroscopic average of
microstructure
Accurate and reliable simulation at macroscopic
scale
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