My research concerns with analytical methods in few domains of mathematics. I have been working on divisors and quasi-conformal maps on Riemann surfaces, ergodic theorems for sums of operators, distribution of eigenvalues of quantum statistical mechanics Hamiltonians, Anderson localization for quasi-periodic and random potentials. Currently I am working on applications of Anderson localization to integrable non-linear partial differential differential equations.
Spectral theory of Schroedinger operators and localization
Awards and Grants:
- Guggenheim Fellowship, 2007