Dawei Chen
Boston College
Title
Moduli of Differentials and AI
Abstract
Differentials on Riemann surfaces correspond to translation surfaces with cone points, where the zero orders of differentials determine the cone angles of translation surfaces. Affine transformations act on translation surfaces and preserve the zero type. These perspectives make differentials and their moduli spaces extensively studied in many areas. In this talk, I’ll first introduce the background of differentials and their moduli spaces. Then I’ll explain several recent AI-assisted works relevant to moduli spaces of differentials, which include elementary number theory, automorphisms of Riemann surfaces, topology of hyperplane arrangements, and special generating functions. These AI works were not prompted by me, and they are not as fancy as the million-dollar problems. However, the related questions naturally arose in my research field, and I did think about them before the era of AI. Both parts of the talk should be accessible to a general audience.
