Title:    Non-Vanishing Homology of the Matching Complex

Abstract:     A matching on a graph G is any subgraph where the maximum vertex degree is 1.  Since edge-deletion preserves the property of being a matching, the set of all matchings on G forms a simplicial complex M(G).  We will survey results on the lowest non-vanishing homology group for M(K_n) and, time permitting, discuss the extension of these results to more general graphs.  ​This is a practice talk for my qualifying exam, but no prior familiarity with simplicial complexes nor homology is assumed.

Pizza at 4:00 p.m., talk at 4:15 p.m.