一、题目

Multiplicative Jensen's formula and quantitative global theory for one-frequency Schrödinger operators

二、主讲人

周麒

三、摘要

We explore Avila's global theory for one-frequency Schrödinger operators from the point of view of Aubry duality. We establish the one-to-one correspondence between the Lyapunov exponent of the Schrödinger cocycles and the Lyapunov exponents of its dual cocycles. We also give a new equivalent definition of subcritical, critical, supercritical regimes. Especially, we prove that the acceleration of the Schrödinger cocycle equals to the pair of zero Lyapunov exponents of its dual cocycle. Finally, we talk about its physical application.

四、主讲人介绍

周麒，南开大学陈省身数学研究所教授，曾获天津市杰出青年基金。研究领域为动力系统与数学物理，主要研究方向为拟周期薛定谔算子谱理论。已在Duke Math J, Ann. Sci. Ec. Norm. Super, Adv Math, Phy Rev Lett, Comm Math Phys等期刊发表多篇论文。

五、邀请人

胡锡俊 数学学院教授

六、时间

11月18日（周四）15:00-15:50

七、地点

中心校区知新楼B座924报告厅

八、主办方

山东大学数学学院