19/02/2019, 10:00 — 11:00 — Room P3.10, Mathematics Building
San Vũ Ngọc, IRMAR, Université de Rennes 1
Microlocal analysis, quantization and integrable systems (II)
In the second lecture, I will show how to develop a full microlocal theory: how to localize quantum mechanics in phase space? Using the notion of semiclassical wavefront set, we obtain a very flexible calculus that can be used to prove Bohr-Sommerfeld rules at any order for a very accurate description of the spectrum of semiclassical operators. I will also give a quick overview of what can be done for non selfadjoint operators using Sjöstrand's theory of complexified phase spaces.
- Terry Tao blog on Weyl quantization
- S. Vũ Ngọc, Symplectic Techniques for Semiclassical Completely Integrable Systems, 2005
- S. Vũ Ngọc, Systèmes intégrables semi-classiques: du local au global, 2006
- D. Sepe and S. Vũ Ngọc, Integrable systems, symmetries, and quantization, 2017