Volumes and intersection theory on moduli spaces of differentials
Computing volumes of moduli spaces has significance in many fields. For instance, the celebrated Witten's conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volumes, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten's intersection numbers on moduli spaces of holomorphic differentials to compute the Masur-Veech volumes induced by the flat metric of the differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).