My research lies between analysis and geometry. I study the geometric quantization of Kähler compact manifolds and its semi-classical limit. Besides developing the foundations of the theory, I am also interested in its applications, as for instance, in spectral theory or topological quantum field theory, and in its relations with symplectic topology.
As regards geometry, I use essentially symplectic geometry (geometric quantization, integrable systems, symplectic reduction). As regards analysis, I have a detailed knowledge of microlocal analysis (Toeplitz operators, Pseudo-differential operators, Fourier integral operators).
For the past few years, I have been studying the semiclassical limit of the Chern-Simons topological quantum field theories. The classical part of the theory deals with moduli spaces of flat bundles on surfaces and 3-dimensional manifolds. The quantum part belongs more to 3-dimensional topology including Jones polynomial and Witten-Reshetikhin-Turaev (WRT) invariant. I work mainly on the Witten conjecture about the asymptotic behavior of the WRT invariants. More generally I try to understand the semi-classical limit of quantum invariants associated to cobordisms, including the quantum representations of the mapping class group.
J'ai soutenu mon habilitation en mai 2014, le mémoire, les transparents.