# Analysis Seminar

## A spectral gap in $\mathrm{SL}^2(\mathbb R)$ and applications: expansion, Furstenberg measures and the Anderson-Bernoulli model

Jean Bourgain
IBM von Neumann Professor, School of Mathematics
November 30, 2016

## The hidden landscape of localization of eigenfunctions

Svitlana Mayboroda
University of Minnesota
March 8, 2016
Numerous manifestations of wave localization permeate acoustics, quantum physics, mechanical and energy engineering. It was used in construction of noise abatement walls, LEDs, optical devices, to mention just a few applications. Yet, no systematic methods could predict the exact spatial location and frequencies of the localized waves.

## Supersymmetric approach to random band matrices

Tatyana Shcherbyna
Member, School of Mathematics
March 2, 2016
Random band matrices (RBM) are natural intermediate models to study eigenvalue statistics and quantum propagation in disordered systems, since they interpolate between mean-field type Wigner matrices and random Schrodinger operators. In particular, RBM can be used to model the Anderson metal-insulator phase transition even in 1d. In this talk we will discuss an application of the supersymmetric method (SUSY) to the analysis of the bulk local regime of some specific types of RBM.