Bellow Lecture Series

Title: Treating small denominators without KAM
Speaker: Svetlana Jitomirskaya
Speaker Info: UC Irvine
Brief Description:
Special Note:

Small denominator problems appear in various areas of analysis, PDE, and dynamical systems, including spectral theory of quasiperiodic Schrödinger operators, non-linear Schrödinger equations, and non-linear wave equations. These problems have traditionally been approached by KAM-type constructions. We will discuss the new methods, originally developed in the spectral theory of quasiperiodic Schrödinger operators, that are both considerably simpler and lead to results completely unattainable through KAM techniques. For quasiperiodic operators, these methods have enabled precise treatment of various types of resonances and their combinations, leading to proofs of sharp (arithmetic) spectral transitions, the ten martini problem, and the discovery of universal hierarchical structures of eigenfunctions.
Date: Wednesday, October 19, 2022
Time: 04:00pm
Where: Lunt 105
Contact Person: Ben Weinkove
Contact email: weinkove@math.northwestern.edu
Contact Phone:
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