English

No Where to Go But High: A Perspective on High Dimensional Expanders

Combinatorics 2023-05-23 v2 Computational Complexity

Abstract

"No Where to go but in" is a well known statement of Osho. Osho meant to say that the answers to all our questions should be obtained by looking into ourselves. In a paraphrase to Osho's statement we say "No Where to go but high". This meant to demonstrate that for various seemingly unrelated topics and questions the only way to get significant progress is via the prism of a new philosophy (new field) called high dimensional expansion. In this note we give an introduction \footnote{This introduction reflects the authors' interests and by no mean claim to represent the field in a through way} to the high dimensional expansion philosophy, and how it has been useful recently in obtaining progress in various questions in seemingly unrelated fields. This exposition is dedicated to the memory of my mother, Sarah Kaufman, who was always trying to understand the reason why things behave in a certain way. It is also dedicated to the memory of my father Eliezer Kaufman.

Keywords

Cite

@article{arxiv.2304.10106,
  title  = {No Where to Go But High: A Perspective on High Dimensional Expanders},
  author = {Roy Gotlib and Tali Kaufman},
  journal= {arXiv preprint arXiv:2304.10106},
  year   = {2023}
}

Comments

Submitted to Proceedings of the ICM 2022