I will give an introductory talk on super Riemann surfaces, and the two types of punctures one sees on them, NS and Ramond punctures. I will describe how a super Riemann surfaces determines a
spin curve, and, why in some special cases, a spin curve determines a super Riemann surface. I willthen define the moduli space of super Riemann surfaces, called supermoduli space, and answer two
important questions about it: (1) Is the supermoduli space just the same thing as the moduli space of spin curves (Teaser: No), and (2) Is the supermoduli space a vector bundle over the moduli
space of spin curves? The answer to this question–also, no– was given in the NS punctured case by Donagi and Witten in 2014, and Ron and I have recently proved it in the case of Ramond punctures.
I will sketch the proof of this result, but try to keep it introductory by focusing on how the proof adapts classical algebraic geometry to the super case, e.g., branched covers and computing tangent
spaces using deformation theory. Now that we know a bit about supermoduli space, what should we do with it? The answer is, compute its volume– appropriately measured– so that physicists can
compute some probabilities. Studying this measure is an active area of research in supergeometry, and I will, time-permitting, outline some of the main problems.