Lingrui Ge (UCI)

Quantitative almost reducibility and its spectral applications


We report our recent progresses on quantitative almost reducibility (QAR) for quasiperiodic $SL(2,\R)$-cocycles. As applications, we will explain how to use QAR to obtain arithmetic version of Anderson localization, exponential dynamical localization, ballistic transport, asymptotical estimates of spectral gaps and universal hierarchical structure of generalized eigenfunctions for quasiperiodic Schr\"odinger operators (especially for the almost Mathieu operator).

This is based on joint works with Ilya Kachkovskiy, Jiangong You, Xin Zhao and Qi Zhou.