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Abstract

Expander graphs in general, and Ramanujan graphs in particular, have played an important role in computer science and pure mathematics in the last four decades. In recent years the area of high dimensional expanders (i.e. simplical complexes with properties generalizing those of expanding graphs) and Ramanujan complexes is starting to emerge. The various motivations of this subarea will be surveyed: these include connections and applications to cohomology and Gromov's overlapping problem on the pure math side and to property testing and error correcting codes on the CS side.