Almost every talk on translation surfaces starts with a double pentagon or with an octagon. But are these n-gons generic examples of translation surfaces? That is, how likely is it that if we choose a translation surface of genus 2, it will look similar to one of them?
Inspired by this question, we are interested in the expected value of geometric properties of translation surfaces for large genus.
I will define translation surfaces, strata, Masur-Veech measure, ... (as and when required by the audience) and explain how to approach this question for the diameter of a surface. This is based on joint work with Howie Masur and Kasra Rafi from 2018.
