Maria Gillespie: Lazy Tournaments and Moduli of Curves

Combinatorics has increasingly been appearing as an essential tool in algebraic geometry, as more abstract geometric problems are shown to boil down to a simple combinatorial rule. We discuss the methods of combinatorial algebraic geometry in general, and then describe a new recent example of this phenomenon involving an algorithm on trees called a "lazy tournament", and how it helps us understand the moduli space of genus zero stable curves.