Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

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 recent years, they have gained importance in their own right, appearing in areas such as representation theory, geometric group theory, tropical geometry, and lately reinterpreted as spaces of phylogenetic networks. In particular, they resolve the singularities of tree spaces studied by Billera, Holmes, and Vogtmann.