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{\Large Department of Mathematics, BGU}

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\textbf{On} \emph{Tuesday, January 10, 2023}
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\textbf{At} \emph{15:00 -- 16:00}
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\textbf{In} \emph{-101}

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{\large\scshape Adam Logan 
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  (McGill)
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will talk about
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{\Large\bfseries A conjectural uniform construction of many rigid Calabi-Yau threefolds\par}
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\textsc{Abstract:}
Given a rational Hecke eigenform \$f\$ of weight \$2\$, Eichler-Shimura theory gives a construction of an elliptic curve over \$\{\textbackslash{}mathbb Q\}\$ whose associated modular form is \$f\$.  Mazur, van Straten, and others have asked whether there is an analogous construction for Hecke eigenforms \$f\$ of weight \$k\textgreater{}2\$ that produces a variety for which the Galois representation on its etale \$\{\textbackslash{}mathrm H\}\^{}\{k-1\}\$ (modulo classes of cycles if \$k\$ is odd) is that of \$f\$.  In weight \$3\$ this is understood by work of Elkies and Sch"utt, but in higher weight it remains mysterious, despite many examples in weight \$4\$.  In this talk I will present a new construction based on families of K3 surfaces of Picard number \$19\$ that recovers many existing examples in weight \$4\$ and produces almost \$20\$ new ones.





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{\bfseries Please Note the Unusual Time!}
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