what does it mean to pick a ``random'' hyperbolic surface, and how does one even go about ``picking'' one? mirzakhani gave an inductive answer to this question by gluing together smaller random surfaces along long curves; this is equivalent to studying the equidistribution of certain sets inside the moduli space of hyperbolic surfaces. starting from first concepts, in this talk i’ll explain a new method for building random hyperbolic surfaces by building random \emph{flat} ones. as time permits, we will also discuss the application of this technique to mirzakhani’s ``twist torus conjecture.'' this is joint work (in progress) with james farre.