Ramanujan Complexes and High Dimensional Expanders

TL;DR

This paper discusses the generalization of expander graphs, especially Ramanujan graphs, to higher-dimensional simplicial complexes, highlighting recent research efforts and potential applications.

Contribution

It provides an overview of recent developments in extending expander graph concepts to high-dimensional complexes, a relatively new area of study.

Findings

Generalization of Ramanujan graphs to high-dimensional complexes

Recent research efforts in high-dimensional expanders

Potential applications in computer science and mathematics

Abstract

Expander graphs in general, and Ramanujan graphs in particular, have been of great interest in the last three decades with many applications in computer science, combinatorics and even pure mathematics. In these notes we describe various efforts made in recent years to generalize these notions from graphs to higher dimensional simplicial complexes.