Kamyrn Spinelli (Queen's University)

Calabi-Yau Manifolds Seminar

Speaker: Kamryn Spinelli (Queen's University)

Title: What's Calabi-Yau about Calabi-Yau modular forms?

Abstract: Connections between elliptic curves and modular forms have been well-known for many years. The analogous picture in higher dimensions is less clear even though there is strong evidence, especially in the context of mirror symmetry, that these physically-motivated geometric objects (Calabi-Yau varieties) and arithmetic objects (modular forms and their generalizations) know something about each other. In a sequence of articles beginning in 2011, Movasati initiated a program to systematically understand these connections in the case of quintic threefolds. Toward this end, he introduced a generalization of modular forms called (differential) Calabi-Yau modular forms. In this talk, we will survey the ingredients in the context of elliptic curves, before turning to the quintic threefold and Movasati's definition of Calabi-Yau modular forms.