Expanders are a family of finite graphs that are sparse but
highly connected. The first explicit examples of expanders were
quotients of a Cayley graph of a discrete group with Property (T) by
finite index subgroups. This was due to Margulis. In recent years,
higher dimensional generalizations of expander graphs (family of
simplicial complexes of a fixed dimension) have received much attention.
I will talk about a generalization of Margulis’ group theoretic
construction that replaces expanders by one of its higher analogs.