Conference abstracts

Session S07 - Finite Fields

July 29, 17:30 ~ 17:55

Arithmetic Mirror Symmetry of K3 Surfaces and Hypergeometric Functions.

Adriana Salerno

Bates College, USA   -

Mirror symmetry predicts surprising geometric correspondences between distinct families of algebraic varieties. In some cases, these correspondences have arithmetic consequences. Among the arithmetic correspondences predicted by mirror symmetry are correspondences between point counts over finite fields. In particular, we explore closed formulas for the point counts for our alternate mirror families of K3 surfaces, their relation to their Picard-Fuchs equations and hypergeometric functions.

Joint work with Charles Doran (University of Alberta, Canada), Tyler Kelly (University of Cambridge, UK), Steven Sperber (University of Minnesota, USA), John Voight (Dartmouth College, USA) and Ursula Whitcher (University of Wisconsin, Eau Claire, USA).

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