Studying the statistical behavior of number theoretic quantities is presently in vogue. The proof of the Sato-Tate Conjecture on point counts of a fixed elliptic curve over finite fields by Richard Taylor (and collaborators) is one of the most significant recent results in the field. Here we discuss point counts in another aspect, for "hypergeometric families" of elliptic curves and K3 surfaces. We obtain Sato-Tate distributions for these families, which turn out to be of SU(2) type (a.k.a. semicircular) and of O3 type (a.k.a. Batman type). Speaker(s): Ken Ono (University of Virginia)
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