The topology of moduli spaces of graphs Seminar

Finite metric graphs paramaterize many phenomena in mathematics and science, so we would like to understand spaces which parameterize such graphs, i.e. moduli spaces of graphs. Moduli space of graphs with a fixed number of loops and leaves often have interesting topology 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.