|Title: Selmer groups, ranks of elliptic curves, and applications|
|Speaker: Ari Shnidman of Boston College|
|Contact: David Zureick-Brown, firstname.lastname@example.org|
|Date: 2019-01-22 at 4:00PM|
|Venue: MSC W201|
I'll discuss some forthcoming results on Selmer groups in twist families of elliptic curves. In work with Lemke Oliver, we bound the average size of the 2-Selmer group in quadratic twist families, when E(Q) = 0. This bounds the average Mordell-Weil rank in such families. I'll also discuss work with Alpoge and Bhargava on Selmer groups of sextic twists of elliptic curves, with an application to a question about cubic fields.
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