报告人：周麒（南开大学陈省身数学研究所）

时 间：2026年10月10日10:30

地 点：海韵园实验楼S102

内容摘要:

The Almost Mathieu Operator (AMO) is a canonical mathematical model for the quantum Hall effect. In the 1970s, Hofstadter numerically computed the spectrum of the AMO, yielding the iconic Hofstadter's Butterfly—a structure widely recognized in physics. Recent experimental work by physicists has confirmed the existence of the Hofstadter's Butterfly. Rigorously proving this structure mathematically remains a long-standing open problem known as the Dry Ten Martini Problem, which is closely tied to Thouless’s Nobel Prize-winning research. For non-critical AMOs, it has been established that all spectral gaps are open. While Argentieri-Avila demonstrated that the Dry Ten Martini Problem is unstable in the subcritical regime, our work proves its robustness in the supercritical regime.

个人简介：

周麒，南开大学陈省身数学研究所教授。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。受邀在 2024 年度国际数学物理大会（ICMP）上做邀请报告。在Duke Math. J, Ann Sci ENS, Cambridge J Math, Math. Ann, Adv.Math, PRL, CMP 多篇论文。

联系人：朱玉峻