Research interests
My research focuses on the development of semiclassical methods on manifolds, with applications to spectral theory. Basically, the goal is to interpret various asympotical regimes in spectral theory (large total spin, large number of particles) as a semiclassical limit. During my PhD, I have contributed to the framework of Berezin-Toeplitz quantization in order to study the large spin limit of systems with a fixed number of particles. Toeplitz operators allow one to make sense of the usual two-dimensional sphere (for instance) as a configuration space of positions and momenta, to find a quantum equivalent of classical hamiltonians, and to study these quantum hamiltonians in the semiclassical limit.
Research articles
All of my publications and prepublications can be found on arXiv, and a subset can be found on HAL.
Publications
- Universality for free fermions and the local Weyl law for semiclassical Schrödinger operators, with Gaultier Lambert, Journal of the European Mathematical Society, accepted for publication
- WKB eigenmode construction for analytic Toeplitz operators, Pure and Applied Analysis 5 (2), pp. 213-260.
- A direct approach to the analytic Bergman projection, Annales de la Faculté des Sciences de Toulouse, accepted for publication. with Michael Hitrik and Johannes Sjöstrand
- Fractional exponential decay in the forbidden region for Toeplitz operators, Documenta Mathematica 25, 1315–1351 (2020)
- Uniform spectral asymptotics for semiclassical wells on phase space loops (with San Vũ Ngọc), Indagationes Mathematicae 32(1), 3–32 (2021)
- Toeplitz operators with analytic symbols, Journal of Geometric Analysis, 31:3915–3967, 2021
- Low-energy spectrum of Toeplitz operators with a miniwell, Communications in Mathematical Physics, 378(3), 1587–1647 (2020)
- Low-energy spectrum of Toeplitz operators: the case of wells, Journal of Spectral Theory, Vol. 9 no 1, pp. 79-125
Prepublications
- The Szegö kernel in analytic regularity and analytic Fourier Integral Operators
- Central limit theorem for smooth statistics of one-dimensional free fermions, with Gaultier Lambert
- Real-analytic geodesics in the Mabuchi space of Kähler metrics and quantization, with Steve Zelditch
- The Bergman kernel in constant curvature
- Quantum selection for spin systems
Dissertations
- PhD thesis: The low-energy spectrum of Toeplitz operators, 2019
- Masters thesis: Projecteur de Szegö et théorème de Kodaira, 2015 (in French)
Working group "Principes d'incertitude et prolongement unique"
Below are some notes (in French) of a working group at IRMA during the academic year 2017-2018
Other
Here is a library, and here is my Github page.