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Classical hypergeometry and the modularity of Calabi-Yau manifolds

Banff International Research Station for Mathematical Innovation and Discovery

In my talk I will examine instances of modularity of (rigid) Calabi--Yau manifolds whose periods are expressed in terms of hypergeometric functions. The $p$-th coefficients $a(p)$ of the corresponding modular form can be often read off, at least conjecturally, from the truncated partial sums of the underlying hypergeometric series modulo a power of $p$ and from Weil's bounds. I will also discuss some hypergeometric features that relate the non-truncated sums---the periods, to the critical $L$-values of the modular forms.

Mathematics; Number theory; Algebraic geometry

video/mp4

Author affiliation: The University of Newcastle

2017-03-31

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61067

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/