This study group has the aim to make the PhD students in Analysis to meet and talk about math together, everybody is welcome. 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 florent.noisette@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; Zakharov's book on turbulence
• kinetic equations theory, for example with kinetic schemes in numerical analysis : Godlewski's & raviart's book
• physics session on Schrodinger : microscopic mode, potential wells, hydrogen model and atom interactions
• equations of general relativity : Maxwell, Lorentzian change of variable, Ricatti equation

Year 2020-2021 :

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 and stricharzt estimates" 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 Zreik
• 04-16-2021 : Chapter 6 : "Global existence and finite time blow-up" by Thomas Normand
• 05-07-2021 : Chapter 4 : "Local existence" by Florent Noisette

Cycle 3: Miscellaneous

Summary : Until the end of the year, we will have independant session on various thematics.

• 05-14-2021 : "Global existence for Klein Gordon using normal form" by Pierre Brun
• 27-05-2021 : "Metropolis algorithm" by Laurent Michel
• 04-05-2021 : "Metropolis algorithm" by Laurent Michel

Year 2021-2022 :

Cycle 1 : Introduction to control theory

Summary : the goal is to discover together the basics of control theory. The reference will be Coron's and Tucsnak's books.

• 01-10-2021 : "introduction and finite dimensional system"  by Florent Noisette
• 08-10-2021 : "controlabilité, définitions des différentes notions" by Adrien Tendani Soler
• 15-10-2021 : "observabilité, définitions des différentes notions" by Matthieu Pauron
• 12-11-2021 : "admissibility condition for observability and controlability" by Pedro Jaramillo
• 19-11-2021 : "controlability for the wave equation" by Nacer Aarach
• 03-12-2021 : "reachable state for the heat equation" by Thomas Normand (own work)
• 17-12-2021 : "controlability for the heat equation" by Lotfi Thabouti
• 14-01-2022 : "control for NSK" by Adrien Tendani Soler (own work)
• 28-01-2022:  "ingham's theorem and observability for the wave equation" by Florent Noisette

Cycle 2 : Differential geometry in PDE

Summary : the goal is to learn the fundamentals for diffenrential geometry in view of application to PDE. The reference will be Jost's and Lee's books.

• 11-03-2022 : "introduction to manifold"  by Magalie Bénéfice
• 18-03-2022 : "notion de métrique" by Thomas Normand
• 25-03-2022 : "notion of geodesic and normal coordinates" by Florent Noisette
• 01-04-2022 : "existence of geodesic for compact manifold" by Florent Noisette
• 08-04-2022 : "flot de la chaleur" by Magalie Bénéfice
• 15-04-2022 : "vector bundles" by Pedro Jaramillo
• 22-04-2022 : "integral curves" by Matthieu Pauron
• 29-04-2022 : "symplectic structure" by Thomas Normand
• 12-05-2022 : "Lie algebras" by Lotfi Thabouti
• 13-05-2022 : "Lie Groups" by Adrien Tendani-Soler
• 20-05-2022 : "Laplace Operator" By Lotfi Thabouti
• 23-05-2022 : "Laplace Operator" by Lotfi Thabouti
• 27-05-2022 : "Notion of Connection" by Adrien Tendani-Soler
• 10-06-2022 : "Notion of Connection" by Pedro Jaramillo
• 24-06-2022 : "Levi-Civita and curvature" by Magalie Bénéfice
• 01-07-2022 : "Geometry of submanifold" by Matthieu Pauron