This page gathers all the information on the PhD students study group of the PDE team at the IMB. The study group usually meets on friday afternoon at 2PM in various rooms. There is a mailing list you can join by asking me at matthieu.pauron@math.u-bordeaux.fr.

Format : the lecturer assumes that the attendees have at least skimmed through the material he/she is supposed to present. The talk is usually between one and two hour long, and can be divided in several sessions if needed.

If you attend the study group and you believe that there is a permanent member of the team who could provide interesting insight about the next lecture topic, you can ask them during Tuesday's team seminar.

For the permanents members of the team : the study group welcomes any suggestion for a presentation on the topic of the current/past/future lectures, or on something you believe could be of interest to us. Please contact me if you have any idea of such a talk.

Ideas of subjects :

• Kolmogorov's turbulence theory and/or oceanography related topics : Batchelor's book on homogeneous turbulence, Hasselmann's book on ocean waves or Zakharov's book on turbulence,
• kinetic equations theory, for example with kinetic schemes in numerical analysis : Glolewski & Raviart's book
• theory of (completely) integrable functions : articles of Lax & Miura. Idea of the session : Florent presents in the first half and in the second half a permanent member of the team discusses a research topic linked to the notion of integrability.
• physics session on Schrodinger : microscopic mode, potential wells, hydrogen model and atom interactions
• equations of general relativity : Maxwell, Lorentzian change of variable, Ricatti equation,

Cycle 1 : Microlocal analysis

Summary : the goal is to review the basis of the symbolic calculus and the main results on pseudo-differential operators. The main reference is the lecture notes by Thomas Alazard.

• 12-04-2020 : lecture by Thomas Normand on symbols and continuity of pseudo-differential operators
• 12-11-2020 : lecture by Matthieu Pauron on oscillatory integrals
• 12-17-2020 : lecture by Florent Noisette on symbolic calculus and adjointness of pseudo-differential operators
• 01-22-2021 : lecture by Pei Su on applications by the symbolic calculus
• 02-02-2021 : lectures by Matthieu Pauron on the pseudo-differential hyperbolic Cauchy problem,
• 02-12-2021 : lecture by Thomas Normand on microlocal singularities

Cycle 2 : Dispersive equations

Summary : the goal is to follow the book by Cazenave on Nonlinear Schrödinger equations and to get to know the basics of dispersive equations. Other references include Tao's book.

• 03-05-2021 : introductory lecture by Matthieu Pauron
• 03-19-2021 : chapter 2 "The linear Schrödinger equation" by Florent Noisette
• 03-30-2021 : first half of the chapter 3 "The Cauchy problem on a general domain" by Florent Noisette
• 04-09-2021 : second half of the chapter 3 "The Cauchy problem on a general domain" by Mahdi Zrei