I defended my Ph.D. thesis at the University of Bordeaux on May 12th, 2017 under the supervision of Pr. Mouez Dimassi.

**My Ph.D. thesis**

Spectral Analysis of Systems of h-pseudodifferential Operators

**Research Interests**

My research lies in the areas of *Partial Differential Equations* and *Mathematical Physics, *more specifically, in *Semiclassical and Microlocal Analysis, Spectral theory, Scattering theory, *and *Quantum dynamics. *I am mainly interested in the following topics:

**Semiclassical approximation of quantum dynamics**: time evolution of quantum observables, correspondance principle, propagation of coherent states and wave packets.**Spectral and scattering theory for quantum Hamiltonians**: perturbation theory, asymptotic analysis of eigenvalues and resonances, trace formulas, spectral shift function, magnetic Hamiltonians.**Energy-level crossings in quantum mechanics**: systems of h-pseudodifferential operators, Born-Oppenheimer approximation, propagation through energy-level crossings.

**Publications**

1. Long time semiclassical Egorov theorem for h-pseudodifferential systems

**Asymptotic Analysis, Vol 101 (2017), no. 1-2, 17-67.**

2. Semiclassical Trace Formula and Spectral Shift Function for Systems via a Stationary Approach, with M. Dimassi and S. Fujiié.

**International Mathematics Research Notices (2017).**

**Work in progress**

- Lieb-Thirring inequalities and discrete spectrum in gaps for slowly varying perturbations of periodic Schrödinger operators, with M. Dimassi.