Abstract:

In the 1960's, Deligne, Mumford and Knudsen wrote seminal papers about the compactification of moduli spaces of "stable n-pointed curves". The simplest example occurs when one takes n distinct points on the projective line P^1 and considers their isomorphism classes under Möbius transformations. Compactifying the space of isomorphism classes of such n-tuples boils down to define suitable limits as some of the points come together and coalesce. The mentioned papers use quite a bit of machinery from algebraic geometry. We will present a down-to-earth approach using phylogenetic trees. They play the role of a manual (Bedienungsanleitung) for finding proofs: combinatorial manipulations with the trees result in outlines of proofs which then just have to be formulated rigorously in algebraic terms. It is almost miraculous how nicely this works. The talk is understandable for Master's students. This second part of the lectures about moduli spaces does not presuppose having attended the first half.