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{\Large Department of Mathematics, BGU}

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{\Huge AGNT}\\[0.2\baselineskip]

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\textbf{On} \emph{Wednesday, January  1, 2020}
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\textbf{At} \emph{15:00 -- 16:15}
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\textbf{In} \emph{-101}

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{\large\scshape Ari Shnidman 
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  (HUJI)
}
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will talk about
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{\Large\bfseries Monogenic cubic fields and local obstructions\par}
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\textsc{Abstract:}
A number field is monogenic if its ring of integers is generated by a single element.  It is conjectured that 0\% of degree d number fields are monogenic (for any d \textgreater{} 2).  There are local obstructions that force this proportion to be \textless{} 100\%, but beyond this very little is known.  I'll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are still not monogenic.  This uses new results on integral points and ranks of Selmer groups of elliptic curves in twist families.








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