Nowhere to go but high: a perspective on high-dimensional expanders

Abstract

“Nowhere 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 “Nowhere to go but high.” This is 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 to the high-dimensional expansion philosophy, and how it has been useful recently in obtaining progress in various questions in seemingly unrelated fields.