Phylogenetic networks and real moduli spaces
11:00:00 - 12:00:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)
Infused with visual imagery, this talk is motivated by the moduli spaces of punctured Riemann spheres. In the 1970s, Grothendieck, Deligne, and Mumford constructed their compactification using Geometric Invariant Theory. In the 1990s, Gromov and Witten utilized them as invariants arising from string field theory and quantum cohomology. We consider real points of these spaces, which have elegant geometric and combinatorial properties, being compact hyperbolic manifolds with a beautiful tessellation by convex polytopes. In particular, they resolve the singularities of tree spaces studied by Billera, Holmes, and Vogtmann, resulting in a map between real and tropical moduli spaces of curves.