Research interests

Keywords: Semiclassical/microlocal analysis, spectral theory, WKB constructions, normal forms, Born-Oppenheimer approximation.

My research focuses on spectral theory of (pseudo-)differential operators - especially Schrödinger operators - in semiclassical regimes (e.g. Born-Oppenheimer approximation). Spectral asymptotics of Schrödinger operators are linked to the underlying classical trajectories associated with the related classical hamiltonian. During my PhD, I studied a matrix-valued operator with intersecting trajectories. The problem may then be reduced via normal forms to a generic microlocal study at those intersections.

Academic background

I conducted my PhD under the supervision of 藤家雪朗 (Setsuro Fujiié) beetween 2022 and 2025 at Ritsumeikan university (立命館大学) in Kusatsu-shi, Japan. My PhD dissertation should be available soon on the repository of Ritsumeikan university. Previously, I studied at the Ecole Normale Supérieure of Rennes and at Rennes 1 university between 2018 and 2022. Some associated resources (master thesis, agrégation⁽¹⁾ resources, etc) are available on the french version of this website.

Contact

• email: vincent.louatron (at) math.ku.dk
• You can find me on the 4th floor of Vibenshuset, Lyngbyvej 2, 2100 Copenhagen.