"Non UBC"@en . "DSpace"@en . "Desjardins, Julie"@en . "2019-03-14T02:04:07Z"@en . "2018-05-28T15:23"@en . "What can we say about the variation of the rank in a family of elliptic curves We know in particular that if infinitely many curves in the family have non-zero rank, then the set of rational points is Zariski dense in the associated elliptic surface.\nWe use a \u00E2 conjectural substitute\u00E2 for the geometric rank (or rather for its parity) : the root number. For a non-isotrivial family, under two analytic number theory conjectures I show that the root number is -1 (resp. +1) for infinitely many curves in the family. On isotrivial families however, the root number may be constant : I describe its behaviour in this case."@en . "https://circle.library.ubc.ca/rest/handle/2429/68693?expand=metadata"@en . "36.0"@en . "video/mp4"@en . ""@en . "Author affiliation: Max Planck Institute for Mathematics"@en . "10.14288/1.0376859"@en . "eng"@en . "Unreviewed"@en . "Vancouver : University of British Columbia Library"@en . "Banff International Research Station for Mathematical Innovation and Discovery"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@en . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en . "Postdoctoral"@en . "BIRS Workshop Lecture Videos (Oaxaca de Ju\u00E1rez (Mexico))"@en . "Mathematics"@en . "Number theory"@en . "Algebraic geometry"@en . "Arithmetic number theory"@en . "Variation of the root number in families of elliptic curves"@en . "Moving Image"@en . "http://hdl.handle.net/2429/68693"@en .