Geometry Seminar

Date: October 4, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Ursula Whitcher, University of Michigan

Title: Zeta functions of alternate mirror Calabi-Yau families

Abstract: Mirror symmetry predicts surprising geometric correspondences between distinct families of algebraic varieties. In some cases, these correspondences have arithmetic consequences. For example, one can use mirror symmetry to explore the structure of the zeta function, which encapsulates information about the number of points on a variety over a finite field. We prove that if two Calabi-Yau invertible pencils in projective space have the same dual weights, then they share a common polynomial factor in their zeta functions related to a hypergeometric Picard-Fuchs differential equation. The polynomial factor is defined over the rational numbers and has degree greater than or equal to the order of the Picard-Fuchs equation. This talk describes joint work with Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, and John Voight.