Résume | Abstract: Finite metric graphs can be used to describe 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. |