"Non UBC"@en .
"DSpace"@en .
"Swanepoel, Konrad"@en .
"2018-08-08T05:01:01Z"@* .
"2018-02-08T10:30"@en .
"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.\n\nSimeon 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 .
"https://circle.library.ubc.ca/rest/handle/2429/66695?expand=metadata"@en .
"31 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: London School of Economics and Political Science"@en .
"Banff (Alta.)"@en .
"10.14288/1.0369739"@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 .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Convex and discrete geometry"@en .
"Combinatorics"@en .
"Space quartics, ordinary planes and coplanar quadruples"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/66695"@en .