Research

Research interests:

• Spectral theory of quasiperiodic Schrodinger operators

• Global theory of quasiperiodic cocycles

• Fractal properties of singular continuous measures

• Transport theory in quantum physics

• Statistical mechanics; Kac equation; and approach to thermodynamic equilibrium

Publications:

• Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles: available here 

• Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background: available here

• (With S. Jitomirskaya) Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators with smooth potentials: available here 

• (with M. Landrigan) Fine dimensional properties of spectral measures: available here

• Fractal dimensions of spectral measures of rank one perturbations of a positive self-adjoint operator: available here