Monthly Archives: April 2016

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.

Peter Hintz (UC Berkeley)

The Analysis and PDE Seminar will take place on Monday, April 18, in room 891, Evans Hall, from 4:10-5:00 pm.

Speaker: Peter Hintz

Title: Finite codimension solvability of quasilinear wave equations

Abstract: I will describe a general framework, applicable on de Sitter and Kerr-de Sitter spacetimes, which allows one to solve quasilinear wave equations globally for restricted initial data even if the linearized operator has exponentially growing modes. As an application, I will revisit the nonlinear stability of de Sitter space in the context of general relativity. This is work in progress with András Vasy.