Speaker：Qi Zhou (Nankai University)

Time：2026-10-10 10: 30

Location：Conference Room S102 at Experiment Building at Haiyun Campus

Abstract:

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.