Phylogenetic Trees and the Moduli of n Points

This lecture presents a combinatorial approach to the Deligne-Mumford-Knudsen compactification of the moduli space of n distinct points on the projective line P1. Explore how to choose a totally symmetric embedding of orbits of generic points into a high-dimensional projective scheme and take the Zariski-closure Xn of the image. Discover how defining equations for Xn are found via cross-ratios, and how phylogenetic trees naturally yield a stratification. Learn about the forgetful map Xn+1 to Xn which exhibits n-pointed stable curves as fibers, arising a posteriori. If time permits, the speaker will sketch the intriguing case of points in P2. This Special Year Seminar is presented by Herwig Hauser from Universität Wien at the Institute for Advanced Study.