Isoperimetric Inequalities for Ramanujan Complexes and Topological Expanders

Understand

Expander graphs have been intensively studied in the last four decades.

• In recent years a high dimensional theory of expanders has emerged, and several variants have been studied.
• Among them stand out coboundary expansion and topological expansion.
• It is known that for every $d$ there are unbounded degree simplicial complexes of dimension $d$ with these properties.