Volume of the moduli space of super Riemann surfaces

In this lecture I will describe a relationship between different approaches to calculating the volume of the moduli space of super hyperbolic surfaces. Stanford and Witten defined the volume of the moduli space of super hyperbolic surfaces via a natural measure on the character variety of a surface into a supergroup. Alternatively, the volume of a symplectic supermanifold can be quite generally expressed in terms of the Euler class of a bundle over an underlying symplectic manifold together with its symplectic form. These two viewpoints lead to a conjectural relationship between a collection of integrals of known cohomology classes over the moduli space of stable Riemann surfaces and the volume of the moduli space of super Riemann surfaces.