MATH Seminar

Title: Selmer groups of elliptic curves
Seminar: Algebra
Speaker: Zev Klagsbrun of University of Wisconsin-Madison
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2013-03-06 at 3:00PM
Venue: W306
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Abstract: Recently, Poonen and Rains proposed heuristics for the distributions of Selmer groups of elliptic curves. Work dating back to Heath-Brown in 1994 suggests that these heuristics should be satisfied within quadratic twist families of elliptic curves as well. I will be presenting results of Mazur, Rubin, and myself showing that, after a parity adjustment, these heuristics are satisfied within quadratic twist families of elliptic curves with an $S_3$ 2-division field. I will also explain how our work challenges the conventional wisdom of Goldfeld’s conjecture about how ranks are distributed within quadratic twist families of elliptic curves over general number fields.