## Analysis and PDE

•  Shiwen Zhang
•  Arithmetic criteria of spectral dimension for quasiperiodic Schrodinger operators.
•  10/31/2016
•  4:02 PM - 4:52 PM
•  C517 Wells Hall

Shiwen Zhang (msu), joint work with Svetlana Jitomirskaya (uci) Abstract: We introduce a notion of &#946;-almost periodicity and prove quantitative lower spectral/ quantum dynamical bounds for general bounded &#946;-almost periodic potentials. Applications include a sharp arithmetic criterion of full spectral dimensionality for analytic quasiperiodic Schrodinger operators in the positive Lyapunov exponent regime and arithmetic criteria for families with zero Lyapunov exponents, with applications to Sturmian potentials and the critical almost Mathieu operator.

## Contact

Department of Mathematics
Michigan State University