---
_id: '14381'
abstract:
- lang: eng
  text: Expander graphs (sparse but highly connected graphs) have, since their inception,
    been the source of deep links between Mathematics and Computer Science as well
    as applications to other areas. In recent years, a fascinating theory of high-dimensional
    expanders has begun to emerge, which is still in a formative stage but has nonetheless
    already lead to a number of striking results. Unlike for graphs, in higher dimensions
    there is a rich array of non-equivalent notions of expansion (coboundary expansion,
    cosystolic expansion, topological expansion, spectral expansion, etc.), with differents
    strengths and applications. In this talk, we will survey this landscape of high-dimensional
    expansion, with a focus on two main results. First, we will present Gromov’s Topological
    Overlap Theorem, which asserts that coboundary expansion (a quantitative version
    of vanishing mod 2 cohomology) implies topological expansion (roughly, the property
    that for every map from a simplicial complex to a manifold of the same dimension,
    the images of a positive fraction of the simplices have a point in common). Second,
    we will outline a construction of bounded degree 2-dimensional topological expanders,
    due to Kaufman, Kazhdan, and Lubotzky.
article_processing_charge: No
article_type: original
author:
- first_name: Uli
  full_name: Wagner, Uli
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
citation:
  ama: Wagner U. High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky,
    and others). <i>Bulletin de la Societe Mathematique de France</i>. 2022;438:281-294.
    doi:<a href="https://doi.org/10.24033/ast.1188">10.24033/ast.1188</a>
  apa: Wagner, U. (2022). High-dimensional expanders (after Gromov, Kaufman, Kazhdan,
    Lubotzky, and others). <i>Bulletin de La Societe Mathematique de France</i>. Societe
    Mathematique de France. <a href="https://doi.org/10.24033/ast.1188">https://doi.org/10.24033/ast.1188</a>
  chicago: Wagner, Uli. “High-Dimensional Expanders (after Gromov, Kaufman, Kazhdan,
    Lubotzky, and Others).” <i>Bulletin de La Societe Mathematique de France</i>.
    Societe Mathematique de France, 2022. <a href="https://doi.org/10.24033/ast.1188">https://doi.org/10.24033/ast.1188</a>.
  ieee: U. Wagner, “High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky,
    and others),” <i>Bulletin de la Societe Mathematique de France</i>, vol. 438.
    Societe Mathematique de France, pp. 281–294, 2022.
  ista: Wagner U. 2022. High-dimensional expanders (after Gromov, Kaufman, Kazhdan,
    Lubotzky, and others). Bulletin de la Societe Mathematique de France. 438, 281–294.
  mla: Wagner, Uli. “High-Dimensional Expanders (after Gromov, Kaufman, Kazhdan, Lubotzky,
    and Others).” <i>Bulletin de La Societe Mathematique de France</i>, vol. 438,
    Societe Mathematique de France, 2022, pp. 281–94, doi:<a href="https://doi.org/10.24033/ast.1188">10.24033/ast.1188</a>.
  short: U. Wagner, Bulletin de La Societe Mathematique de France 438 (2022) 281–294.
date_created: 2023-10-01T22:01:14Z
date_published: 2022-01-01T00:00:00Z
date_updated: 2023-10-03T08:04:03Z
day: '01'
department:
- _id: UlWa
doi: 10.24033/ast.1188
intvolume: '       438'
language:
- iso: eng
month: '01'
oa_version: None
page: 281-294
publication: Bulletin de la Societe Mathematique de France
publication_identifier:
  eissn:
  - 2102-622X
  issn:
  - 0037-9484
publication_status: published
publisher: Societe Mathematique de France
quality_controlled: '1'
scopus_import: '1'
status: public
title: High-dimensional expanders (after Gromov, Kaufman, Kazhdan, Lubotzky, and others)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 438
year: '2022'
...