@prefix vivo: .
@prefix edm: .
@prefix dcterms: .
@prefix dc: .
@prefix skos: .
@prefix ns0: .
vivo:departmentOrSchool "Non UBC"@en ;
edm:dataProvider "DSpace"@en ;
dcterms:creator "Swanepoel, Konrad"@en ;
dcterms:issued "2018-08-08T05:01:01Z"@*, "2018-02-08T10:30"@en ;
dcterms:description """It was shown by Raz-Sharir-De Zeeuw (2016) that the number of coplanar quadruples among n points on an algebraic curve in complex 3-space not containing a planar component or a component of degree 4, is O(n^{8/3}). We complement their result by characterizing the degree 4 space curves in which n points on the curve always have a subcubic number of coplanar quadruples. This also gives a characterization of the plane curves of degree 3 and 4 in which n points on the curve always have a subcubic number of concyclic quadruples. We use the 4-dimensional Elekes-Szabo theorem of Raz-Sharir-De Zeeuw and some old results from classical invariant theory.
Simeon Ball (2016) showed that a set spanning real 3-space, no 3 collinear, with only Kn^2 ordinary planes, lies on the intersection of two quadrics, up to O(K) points. His proof is based on results of Green and Tao, and also generalizes their proof to 3-space. We find a significant simplification of his proof that avoids 3-dimensional dual configurations, using Bezout's theorem and the above-mentioned results from classical invariant theory. This is joint work with Aaron Lin."""@en ;
edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/66695?expand=metadata"@en ;
dcterms:extent "31 minutes"@en ;
dc:format "video/mp4"@en ;
skos:note ""@en, "Author affiliation: London School of Economics and Political Science"@en ;
dcterms:spatial "Banff (Alta.)"@en ;
edm:isShownAt "10.14288/1.0369739"@en ;
dcterms:language "eng"@en ;
ns0:peerReviewStatus "Unreviewed"@en ;
edm:provider "Vancouver : University of British Columbia Library"@en ;
dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ;
dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ;
ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ;
ns0:scholarLevel "Faculty"@en ;
dcterms:isPartOf "BIRS Workshop Lecture Videos (Banff, Alta)"@en ;
dcterms:subject "Mathematics"@en, "Convex and discrete geometry"@en, "Combinatorics"@en ;
dcterms:title "Space quartics, ordinary planes and coplanar quadruples"@en ;
dcterms:type "Moving Image"@en ;
ns0:identifierURI "http://hdl.handle.net/2429/66695"@en .