Several papers have appeared over the past few years investigating the expected topological properties (homology, fundamental group, etc.) of random simplicial complexes. There are various motivations to do so, ranging from discrete analogues of quantum gravity to null models for topological data analysis. An interesting variety of techniques have been applied, including representation theory of the symmetric group, Gromov's local-to-global method for hyperbolicity, and discrete Morse theory. In this talk, I will survey a few of the papers this field, including my own work and joint work with Eric Babson and Chris Hoffman. The talk will aim to be self contained. |