Summer Graduate School
Microlocal analysis originated in the study of linear partial differential equations (PDEs) in the high-frequency regime, through a combination of ideas from Fourier analysis and classical Hamiltonian mechanics. In parallel, similar ideas and methods had been developed since the early times of quantum mechanics, the smallness of Planck’s constant allowing to use semiclassical methods. The junction between these two points of view (microlocal and semiclassical) only emerged in 1970s, and has taken its full place in the PDE community in the last 20 years. This methodology resulted in major advances in the understanding of linear and nonlinear PDEs in the last 50 years. Moreover, microlocal methods continue to find new applications in diverse areas of mathematical analysis, such as the spectral theory of nonselfadjoint operators, scattering theory, and inverse problems.
Thanks to this ever-evolving list of applications of microlocal analysis, it is a favourable time to hold a 2021 Séminaire de Mathématiques Supérieures on the subject. The goal of the SMS is for young mathematicians, particularly graduate students, to have the opportunity to learn key ideas and techniques of the field, with an emphasis on solidifying foundations in view of potential future research. Solving and discussing solutions to exercises provided by lecturers is a key component. The school will benefit advanced master students, PhD students, and early-career researchers with some background in measure theory, functional analysis, partial differential equations, and/or differential geometry.
The SMS is an annual summer school in pure and applied mathematics that has taken place for more than fifty years on the campus of the University of Montreal. Focused on a hot current research topic, the SMS brings together top quality lecturers and students from all over the world. The school is targeted mainly towards advanced graduate students. It consists of roughly 12 courses of around four one-hour lectures, each spread over two weeks. The courses are attended by around 40 to 60 students selected on a competitive basis. The lectures are published in a volume after the end of the meeting.
This school will be held virtually, with courses taking place one day per week throughout the summer.
Basic functional analysis and measure theory courses
For eligibility and how to apply, see the Summer Graduate Schools homepage
This school will require an additional application with SMS directly.