Microlocal analysis

General Informations

Course description


Historical background

Educational team

  • The professor is Christophe Cheverry, see the web page ;
    Office 207/1 in building 23 ; contact : e-mail.

  • The secretariat is provided by Annie Quéméré :
    Office 003 in building 23 ; contact : e-mail.


    The class will be held on Tuesday (from 08h to 10h) and Friday (from 16h15 to 18h15).
    It will take place in building 2A, room 329 (tuesday) and in building 2A, room 313 (friday).
    It starts the 19/10 and stops the 03/12.

Learning materials

    Students will have to refer to their own course notes. We give below some related (recent) references.
    Of course, it should be understood that students can also consult the numerous references therein.
    To complete the course and to broaden his/her knowledge, students can study the following documents.

    - Concerning the part A):
  • The book about Pseudo-differential Operators and the Nash-Moser Theorem by
    P. Gérard (univ. Paris XI) and S. Alinhac is a good classical reference;
  • The books (volumes I, II, ...) about the Analysis of Linear Partial Differential Operators by
    L. Hörmander contain all what is needed;
  • For a general overview on the analysis of partial differential equations, see the lecture notes by
    T. Alazard (ENS). Look especially at the Part 3;
  • Concerning pseudo-differential operators, look for instance at the introduction to this subject by
    J.-M. Bouclet (univ. Toulouse);

    - Concerning the part B):
  • Personal notes about the Stone-Von-Neumann theorem (in french and in english).
    Personal notes about the quantum harmonic oscillator (in french and in english).
  • The quantum harmonic oscillator is discussed (for instance) in the book (Section 6.2) by
    C. Cheverry (univ. Rennes 1) and N. Raymond (univ. Angers). Look also at the following
    (more physical) discussion and at this introduction of the Segal-Bargmann transform;
  • The Fourier uncertainty principle is clearly and shortly explained in this text by
    S. Fushida-Hardy (univ. Stanford);
  • Quantization is discussed in-depth (more deeply that we will do) in the lecture notes by
    S. Bates (univ. Colombia) and A. Weinstein (univ. Berkeley);
  • The Stone Von Neumann theorem is presented for instance in the lecture notes by
    F. Nier (univ. Paris XIII). This text contains many interesting comments;
  • The book about quantum theory for mathematicians by
    Brian C. Hall (univ. Notre Dame) can give a general overview of the aforementioned material.