Abstract

We consider Weil-Petersson volumes of the moduli spaces of conical hyperbolic surfaces. The moduli spaces are parametrised by their cone angles which naturally live inside Hassett's space of stability conditions on pointed curves. The space of stability conditions decomposes into chambers separated by walls. Assigning to each chamber a polynomial corresponding to the Weil-Petersson volume of a moduli space of conical hyperbolic surfaces, we use algebraic geometry to compute wall-crossing polynomials relating the polynomials to each other, and to the volume of the maximal chamber, given by Mirzakhani's polynomial. Time permitting, I will discuss possible future directions.

This is joint work with Anagnostou and Norbury.