# Herwig Hauser - The moduli space of n points on the projective line

Oberseminar: November 4, 2021

#### The moduli space of n points on the projective line $P^1$ - a gentle introduction

The talk will provide a (hopefully pleasant) overview on a recent approach to the Deligne-Mumford-Knudsen moduli space $M_{0,1}$ and its compactification $\bar{M}_{0,n}$ via the theory of phylogenetic trees. It turns out that these purely combinatorial objects optimally codify the limits of n-tuples of points which occur when some of the points come together and coalesce. This provides an amazing interplay between $\bar{M}_{0,n}$ and properties of phylogenetic trees, and, in particular, allows us to reprove the classical theorems in a down-to-earth fashion.

Joint work with Josef Schicho and Jiayue Qi from the University of Linz.