MIT Combinatorics Seminar Homology of the Matching Complex Jakob Jonsson (Massachusetts Institute of Technology) Wednesday, October 4, 2006   4:15 pm    Room 2-136 ABSTRACT A matching in a graph is a set of edges such that no two edges in the set have a vertex in common. The matching complex $M_n$ is the simplicial complex of matchings in the complete graph $K_n$. Bouc provided a complete description of the rational homology of $M_n$, but the integral homology remains a mystery in general. We will give an overview of known properties of this homology and also present some open problems and conjectures.