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.
- Fractional exponential decay in the forbidden region for Toeplitz operators, Doc. Math. 25, 1315–1351 (2020)
- Uniform spectral asymptotics for semiclassical wells on phase space loops (with San Vũ Ngọc), Indag. Math. 32(1), 3–32 (2021)
- Toeplitz operators with analytic symbols, Journal of Geometric Analysis, Advance online publication. doi:10.1007/s12220-020-00419-w
- 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
- A direct approach to the analytic Bergman projection, with Michael Hitrik and Johannes Sjöstrand
- WKB eigenmode construction for analytic Toeplitz operators
- The Bergman kernel in constant curvature
- Quantum selection for spin systems
- 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