The Modularity/Automorphy of Calabi–Yau Varieties of CM type

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• Noriko Yui, Queens University.
• Wednesday 31 May 2017, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Mark Gross.

Abstract: We consider Calabi–Yau varieties of dimension d at most 3 defined over Q, and address the modularity/automorphy question of such Calabi–Yau varieties `a la Langlands. When the dimension of the associated Galois representations are large (for instance, > 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) mod- ularity/automorphy. The presentation is focused on the two examples: • d = 2: K3 surfaces with non-symplectic automorphisms, and • d = 3: Calabi–Yau threefolds of Borcea–Voisin type. If time permits, we will discuss arithmetic mirror symmetry for K3 surfaces.

This talk is part of the Algebraic Geometry Seminar series.

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