January 28: Dawei Chen

Title: Volumes and intersection theory on moduli spaces of Abelian differentials

Abstract:

Computing volumes of moduli spaces has significance in many fields. For instance, the celebrated Witten’s conjecture regarding intersection numbers on the moduli space of curves has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. The initial two other proofs of Witten’s conjecture by Kontsevich and by Okounkov-Pandharipande also used various ideas in ribbon graphs, Gromov-Witten theory, and Hurwitz theory. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials that can be used to compute the Masur-Veech volumes. This is joint work with Martin Moeller, Adrien Sauvaget, and Don Zagier (arXiv:1901.01785).