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SUMMARY:Lingrui Ge (UCI)
DTSTART:20210121T180000Z
DTEND:20210121T190000Z
DTSTAMP:20260423T053015Z
UID:Thouless/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Thouless/3/"
 >Smooth quasiperiodic SL(2\,\\R)-cocycles (I)-Global rigidity results for 
 rotations reducibility and Last's intersection spectrum conjecture.</a>\nb
 y Lingrui Ge (UCI) as part of UCI Mathematical Physics\n\n\nAbstract\nFor 
 quasiperiodic Schr\\"odinger operators with one-frequency analytic potenti
 als\, from dynamical systems side\, it has been proved that the correspond
 ing quasiperiodic Schr\\"odinger cocycle is either rotations reducible or 
 has positive Lyapunov exponent for all irrational frequency and almost eve
 ry energy by Avila-Fayad-Krikorian. From spectral theory side\, the ``Schr
 \\"odinger conjecture"  has been verified by Avila-Fayad-Krikorian and the
  ``Last's intersection spectrum conjecture" has been proved by Jitomirskay
 a-Marx. The proofs of above results crucially depend on the analyticity of
  the potentials. Is analyticity  essential for those problems? Some open p
 roblems in this aspect were raised by  Fayad-Krikorian and Jitomirskaya-Ma
 rx. In this paper\, we prove the above mentioned results for ultra-differe
 ntiable potentials.\n
LOCATION:https://researchseminars.org/talk/Thouless/3/
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