Dry Ten Martini Problem and Hofstadter s Butterfly
主 题: Dry Ten Martini Problem and Hofstadter s Butterfly
报告人: Professor Jiangong You (Nanjing University)
时 间: 2015-05-08 15:00 - 16:00
地 点: 理科一号楼 1114（数学所活动）
Almost Mathieu operator is a typical mathematical model of quantum Hall effect. In 1970 s, Hofstadter diagramed the spectrum of AMO numerically. The diagram is the famous Hofstadter s butterfly in physics. Recently, the Hofstadter s butterfly has been experimentally verified by physicists. To prove it rigorously in mathematics is a long standing open problem called the Dry Ten Martini Problem (also called Ten Martini conjecture by physicists). We solve this problem by methods of dynamical systems, which therefore gives a rigorous mathematical proof for the perfect Cantor structure of the Hofstadter s butterfly. This talk is based on a joint work with A. Avila and Q. Zhou.