ICM大会报告——Small denominators and multiplicative Jensen's formula
报告人：Svetlana Jitomirskaya (Georgia Institute of Technology)
地点：Room 1560, Sciences Building No. 1
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 onsiderably simpler and lead to results completely unattainable through KAM techniques. For one-dimensional 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. The related theory of the dynamics of corresponding linear cocycles leads to a surprising extension of the classical Jensen's formula.