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UID:6f481d1eb3f2242bdc2b819c60700f15
CATEGORIES:Colloquia
CREATED:20230209T101916
SUMMARY:Treating small denominators without KAM
LOCATION:Hill Center Room 705
DESCRIPTION:<p style="background: white;">Abstract: Small denominator problems appear i
 n various areas of analysis, PDE, and dynamical systems, including spectral
  theory of quasiperiodic Schro?dinger operators, non-linear Schro?dinger eq
 uations, and non-linear wave equations. These problems have traditionally b
 een approached by KAM-type constructions. We will discuss the new methods, 
 originally developed in the&nbsp; spectral theory of quasiperiodic Schro?di
 nger operators, that are both considerably simpler and lead to results comp
 letely unattainable through KAM techniques. For quasiperiodic operators, th
 ese methods have enabled precise treatment of various types of resonances a
 nd their combinations, leading to .proofs of sharp (arithmetic) spectral tr
 ansitions, the ten martini problem, and the discovery of universal hierarch
 ical structures of eigenfunctions.</p>
CONTACT:Svetlana Jitomirskaya (UC Irvine)
DTSTAMP:20260826T165125
DTSTART;TZID=America/New_York:20230217T160000
DTEND;TZID=America/New_York:20230217T170000
SEQUENCE:0
TRANSP:OPAQUE
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