Georgia Institute of Technology College of Sciences

A fundamental problem in algebraic geometry is to construct compact moduli spaces parametrizing algebraic shapes. I will discuss a new approach to this problem in the case of Calabi--Yau pairs (X,D) for which D is ample. Such pairs arise from many well-studied algebraic varieties such as plane curves, K3 surfaces, and del Pezzo surfaces. In the case of Calabi-Yau pairs of dimension two, this approach outputs a projective moduli space on which the Hodge line bundle is ample. This is based on joint work with Yuchen Liu that builds on earlier work with Ascher, Bejleri, DeVleming, Inchiostro, Liu, and Wang.