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Motivic Gamma functions and periods associated to the Frobenius method

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Spencer Bloch
University of Chicago/MPIM
Die, 2018-02-20 14:00 - 15:00
MPIM Lecture Hall

(Joint work with Masha Vlasenko) In their work on the Gamma conjecture, Golyshev and Zagier introduced certain inhomogeneous Frobenius solutions defined in a neighborhood of a MUM point of a Landau model. We show in the case of the Apéry family that the variations of these inhomogeneous solutions about a nearby conifold point are periods, and the resulting generating function is a motivic gamma function in the sense of Golyshev. More generally, such solutions yield a variation of \C-Hodge structure on a punctured disk about the MUM point. This variation admits a Q-Hodge structure if the monodromy of the inhomogeneous solutions about the conifold point satisfies the Picard-Lefschetz theorem.

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