Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	尤建功教授，南开大学陈省身数学研究所
Inviter:	郑作环、周喆
Title:	Arithmetic version of Anderson localization via reducibility
Time & Venue:	2019.11.01 10:30-11:30 N202
Abstract:	The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya \cite{J} for the almost Mathieu operators (AMO). Later, the result was generalized by Bourgain and Jitomirskaya to a class of {\it one dimensional} quasi-periodic long-range operators \cite{bj}. In this paper, we propose a novel approach based on an arithmetic version of Aubry duality and quantitative reducibility. Our method enables us to prove the same result for the class of quasi-periodic long-range operators in {\it all dimensions}, which includes \cite{J, bj} as special cases. (with Lingrui Ge).