Speaker: Dr. Rui Han (Louisiana State University)

Title: Schrödinger Cocycles and Avila's Global Theory

Abstract:

A remarkable result in Avila's global theory of quasi-periodic Schrödinger operators is the quantization of acceleration, which measures the slope of the Lyapunov exponent under complexification.

In this talk, we will introduce a characterization of Avila's quantized acceleration in terms of the zeros of finite-volume Dirichlet determinants. We will also discuss applications of this characterization to quasi-periodic Schrödinger operators, including Hölder continuity of the integrated density of states and Anderson localization.

This talk is based on joint work with Wilhelm Schlag.