Svetlana Jitomirskaya (UC Irvine)

The Analysis and PDE Seminar will take place on Monday, May 2, in room 891, Evans Hall, from 4:10-5:00 pm.

Speaker: Svetlana Jitomirskaya

Title: Very small denominators and sharp arithmetic spectral transitions

Abstract: We will discuss two popular discrete quasiperiodic models: the Maryland model and the almost Mathieu operator, both coming from physics. In the regime of positive Lyapunov exponents, spectral properties differ for Diophantine and Liouville frequencies. We will address the question of the location and nature of the corresponding transition, presenting sharp and constructive arithmetic results for both models, that solve some longstanding conjectures. Close to the transition regime, eigenfunctions decay at the non-Lyapunov rate, and we will also present a sharp description of the eigenfunction profile and also of the non-uniformly hyperbolic dynamics of the corresponding transfer-matrix cocycle. The talk is based on works joint with W. Liu.