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 article we survey the history of this area and point out a number of problems that are still open.
| Original language | English |
|---|---|
| Title of host publication | Dynamics, Geometry, Number Theory |
| Subtitle of host publication | The Impact of Margulis on Modern Mathematics |
| Editors | David Fisher, Dmitry Kleinbock, Gregory Soifer |
| Place of Publication | Chicago |
| Publisher | University of Chicago Press |
| Chapter | 7 |
| Pages | 246-275 |
| Number of pages | 30 |
| ISBN (Electronic) | 9780226804163, 022680416X |
| ISBN (Print) | 9780226804026, 9780226804163, 0-226-80402-X |
| State | Published - 1 Feb 2022 |
Keywords
- expander graphs
- spectral gap
- finite simple groups
- equidistribution
- approximate groups
- geometry