Paul Norbury (U of Melbourne)
Measures on the moduli space of curves and super volumes
|Thu, Feb 15, 2024, 15:30 - 17:00
Seminar Room A
In this lecture I will define a family of finite measures on the moduli space of smooth curves with marked points. The measures are defined via a construction analogous to that of the Weil-Petersson metric using the extra data of a spin structure. In fact, the measures arise naturally out of the super Weil-Petersson metric defined over the moduli space of super curves. The total measure can be identified with the volume of the moduli space of super curves. It can be calculated in many examples, and conjecturally satisfies a recursion analogous to Mirzakhani's recursion relations between Weil-Petersson volumes of moduli spaces of hyperbolic surfaces. This conjecture has been verified in many cases, including the so-called Neveu-Schwarz case where it coincides with the recursion of Stanford and Witten. The general case produces deformations of the Neveu-Schwarz volume polynomials, satisfying the same Mirzakhani-like recursion relations.