Hypergraphs with Low Dimension
Any hypergraph can be viewed as an object with geometric properties, by considering a geometric realisation of its associated abstract simplicial complex. It is well-known that any $k$-uniform hypergraph has such a realisation in $(2k-1)$-dimensional real space. We focus in particular on $k$-uniform hypergraphs that have a geometric realisation in $k$-dimensional space (so when $k=2$ this is the class of planar graphs). We consider some properties of planar graphs that naturally extend to this class of ``low-dimensional' hypergraphs.
Penny Haxell, University of Waterloo, Canada