Semiclassical analysis is a set of methods allowing to study partial  differential equations with rapidly oscillating solutions. The first semiclassical tools were developed in the early 20th century by physicists, in order to understand the relation between quantum and  classical mechanics. Since the 1970s, it has become a standard tool in mathematical analysis, through the use of oscillatory integrals and pseudodifferential operators. In the past few years, semiclassical analysis has been increasingly used in numerical analysis of high frequency wave problems, both to understand convergence properties of existing algorithms and to design new ones.

Semiclapp is a summer school meant as an introduction to semiclassical analysis for participants with a minimal background in mathematical analysis of PDEs, and interested in applications involving numerical aspects of wave propagation or quantum mechanics. The school is divided into five lectures of two hours ranging from the presentation of the basic tools of the theory to advanced results. Each lecture, except the last one, is complemented by an exercise section of three hours. Semiclapp will thus focus on practice and applications of semiclassical techniques more than on theoretical aspects. The participants will also have the opportunity of presenting their work in a poster session.

Semiclapp will take place in the Laboratoire J.A. Dieudonné, in Nice, on the Valrose campus, from May 13th to 17th.

It will start on Monday morning around 9 a.m., and finish on Friday around 12 a.m.

Just fill in the form by clicking « my registration » on the left menu. Your registration will be confirmed a few days later by the organizers. We should have a limited amount of funding to pay for the accommodation of the participants, dedicated in priority to the youngest researchers. If you want to benefit from this funding, you can indicate it it the registration link.

For the participants who applied for funding, we should be able to cover their accomodation, by rooms of 2-3, but not their travel.

The deadline for registrations is February 23rd.

1. Tools of semiclassical analysis

Lecture by Melissa Tacy. Exercise session by Simona Rota-Nodari.

2. WKB method, propagation of singularities

Lecture by Jared Wunsch. Exercise session by Antoine Prouff.

3. Introduction to scattering theory

Lecture by Maxime Ingremeau. Exercise session by Zois Moitier.

4. Semiclassical scattering, resolvent estimates

Lecture by Martin Vogel. Exercise Session by David Lafontaine.

5. Semiclassical analysis and boundary conditions

Lecture by Nicolas Burq. No exercise session.

We will have two plenary talks:

• Simon Chandler-Wilde (University of Reading): Old and new wavenumber-explicit estimates for the norms and condition numbers of boundary integral operators in acoustic scattering
• Caroline Lasser (T.U. München): Variational Gaussian approximation for semi-classical quantum dynamics

1. Tools of semiclassical analysis

2. Propagation of singularities: Lecture notes, Exercises, Correction of the exercises

3. Introduction to scattering theory: Lecture notes, exercises and corrections

4. Semiclassical scattering: Lecture notes, Exercise sheet 1, Exercise sheet 2.

Slides of Simon Chandler Wilde's talk.

The schedule can be found below, or downloaded here.

Bruno Desprès

Ilaria Perugia

Euan Spence

Scientific organisation:

Théophile Chaumont-Frelet

Victorita Dolean

Maxime Ingremeau

Administrative organisation:

Amanda Perrino