In lieu of the regular APDE seminar on Monday, 2/7, I would like to advertise the talk of Svetlana Jitomirskaya (UCI), which will be given in-person (740 Evans) and online via Zoom from 4:10pm to 5:00pm PST. The Zoom meeting room link is:
Title: Treating Small Denominators without KAM
Abstract: 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.