Event Type:

Number Theory Seminar

Date/Time:

Tuesday, June 4, 2019 - 16:00 to 16:45

Location:

Weniger 201

Guest Speaker:

Institution:

Bates College

Abstract:

In this talk, we will show the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picardâ€“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, Steven Sperber, John Voight, and Ursula Whitcher.

Host: