Number theory seminar: Noriko Yui

Speaker: Noriko Yui, Queen's University, Kingston, Canada

Title: Modularity/Automorphy of Calabi–Yau Varieties of CM type

Abstract:

We consider Calabi–Yau varieties of dimension d <= 3 defined over Q, and address the modularity/automorphy question of such Calabi–Yau varieties. When the dimension of the associated Galois representations are large, e.g., > 2, the problem poses a serious challenge and is out of reach in the general situations.

In this talk, I will concentrate on Calabi–Yau varieties of CM type, and establish their (motivic) modularity/automorphy. The presentation is focused on the two examples: K3 surfaces with non-symplectic automorphisms, and Calabi–Yau threefolds of Borcea–Voisin type. If time permits, we will discuss arithmetic mirror symmetry for mirror pairs of Calabi–Yau varieties at CM points.