Updated abstract for J. Voight’s talk

The abstract of John Voight’s talk tomorrow got somehow messed up in the announcements. Here is the actual abstract for his talk.

Title: On the hypergeometric decomposition of symmetric K3 quartic pencils

Abstract: We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard–Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write
this in terms of global $L$-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.

This is joint work with Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, and Ursula Whitcher.


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