Year: 2018
Type: preprint
Abstract: Two short seminal papers of Margulis used Kazhdan's property $(T)$ to give, on the one hand, explicit constructions of expander graphs, and to prove, on the other hand, the uniqueness of some invariant means on compact simple Lie groups. These papers opened a rich line of research on expansion and spectral gap phenomena in finite and compact simple groups. In this paper we survey the history of this area and point out a number of problems which are still open.
Source: arXiv (Cornell University)
Authors: Breuillard, Emmanuel, Lubotzky, Alexander
Institution: Hebrew University of Jerusalem
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2830897620