报告题目： Almost reducibility and applications to the spectrum of quasiperiodic Schrodinger operator (1)


报告人  周麒（南京大学）


报告时间 2017年7月25日08:30-09:30

报告地点  维格堂319

报告摘要  In these  talks, we will review recent developments on (almost) reducibility of quasiperiodic SL(2,R) cocycles, and its applications on  quasiperiodic Schrodinger operator. As an first application, we prove the
  Aubry-Andre-Jitomirskaya's conjecture, i.e. for almost Mathieu operator, there is a phase transition line between the singular continuous spectrum and pure point spectrum. This is joint work with A.Avila and J.You.


报告题目：Almost reducibility and applications to the spectrum of quasiperiodic Schrodinger operator (2)

报告人  周麒（南京大学）


报告时间 2017年7月25日09:30-10:30

报告地点  维格堂319

报告摘要  As the second application, we prove  in this transition line, both pure point spectrum and pure singular continuous spectrum can occur  for dense frequency. This is joint with A.Avila and S.Jitomirskaya.

报告题目：Almost reducibility and applications to the spectrum of quasiperiodic Schrodinger operator (3)

报告人  周麒（南京大学）


报告时间 2017年7月25日10:30-11:30

报告地点  维格堂319

报告摘要 As the third application, we discuss recent advances on  Dry  Ten Martini Problem, i.e. for almost Mathieu operator, all the spectral gaps are open. In fact, for non-critical almost Mathieu operators with Diophantine frequency, we can establish the  exponential asymptotics on the size of spectral gaps. This is mainly joint with A.Avila and J,You.