Slides (in english) :

(Prepared with Magicpoint or beamer).

• Edge statistics in dimension 1.



• Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line.



• Universal asymptotic ergodicity of the unfolded eigenvalues and localization centers of random Hamiltonians in the localized regime.



• Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential.



• Gaussian exponential sums.



• Decorrelation estimates for the eigenlevels of random operators in the localized regime.



• Level, level spacings and localization centers statistics in the localized regime.



• Non monotonous random Schrödinger operators.



• Resonances for ``large'' ergodic systems.



• Lifshitz tails for some random Schrödinger operators or an aspect of random walk in random traps.



• Internal Lifshitz tails for the density of surface states of random operators.



• Localization for random quantum graphs.



• Lyapunov exponents and singular continuous spectrum.



• The renormalization of exponential sums and cocycles.



• Resonances for slowly varying perturbations of the periodic Schrödinger equation.



• Resonant tunneling, level repulsion and spectral type for adiabatic quasi-periodic Schrödinger operators.



• Quasi-periodic adiabatic Schrödinger operators - Interacting spectral bands.



• The spectrum of periodic surfacic perturbations of the Schrödinger and Maxwell equations.



• Complex tunneling and Lyapunov exponents for adiabatic quasi-periodic Schrödinger equation.



• Internal Lifshitz tails for random Schrödinger operators.



• A walk through the WKB theory for one dimensional adiabatic quasi-periodic Schrödinger operators.



• Regularity properties for the density of states of random Schrödinger.