# The Gamma and Strominger–Yau–Zaslow conjectures : a tropical approach to periods

@article{Abouzaid2020TheGA, title={The Gamma and Strominger–Yau–Zaslow conjectures : a tropical approach to periods}, author={Mohammed Abouzaid and Sheel Ganatra and Hiroshi Iritani and Nick Sheridan}, journal={Geometry \& Topology}, year={2020} }

We propose a new method to compute asymptotics of periods using tropical geometry, in which the Riemann zeta values appear naturally as error terms in tropicalization. Our method suggests how the Gamma class should arise from the Strominger-Yau-Zaslow conjecture. We use it to give a new proof of (a version of) the Gamma Conjecture for Batyrev pairs of mirror Calabi-Yau hypersurfaces.

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We consider the residual B-model variation of Hodge structure of Iritani defined by a family of toric Calabi–Yau hypersurfaces over a punctured disk
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In this paper we consider the oscillatory integrals on Lefschetz thimbles in the Landau-Ginzburg model as the mirror of a toric Fano manifold. We show these thimbles represent the same relative…

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