Georgia Institute of Technology College of Sciences

Finite metric graphs are used to describe many phenomena in mathematics and science, so we would like to understand the space of all such graphs, which is called the moduli space of graphs. This space is stratified by subspaces consisting of graphs with a fixed number of loops and leaves. These strata generally have complicated structure that is not at all well understood. For example, Euler characteristic calculations indicate a huge number of nontrivial homology classes, but only a very few have actually been found. I will discuss the structure of these moduli spaces, including recent progress on the hunt for homology based on joint work with Jim Conant, Allen Hatcher and Martin Kassabov.