School of Mathematical Sciences

How to build a hypergraph expander menu

How to build a hypergraph expander

David Conlon (University of Oxford)
Fri, 27/10/2017 - 16:00
Queens Building, W316
Seminar series: 

We present a simple mechanism, which can be randomised, for constructing sparse 3-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over elementary abelian 2-groups and have vertex degree which is polylogarithmic in the number of vertices. Their expansion properties, which are derived from the underlying Cayley graphs, include analogues of vertex and edge expansion in graphs, rapid mixing of the random walk on the edges of the skeleton graph, uniform distribution of edges on large vertex subsets and the geometric overlap property.