"Non UBC"@en . "DSpace"@en . "B\u00E1r\u00E1ny, Imre"@en . "2018-08-06T05:02:18Z"@* . "2018-02-06T10:36"@en . "Caratheodory's classic result says that if a point $p$ lies in the convex hull of a set $P \subset R^d$, then it lies in the convex hull of a subset $Q \subset P$ of size at most $d+1$. What happens if we want a subset $Q$ of size $k < d+1$ such that $p \in conv Q$? In general, this is impossible as $conv Q$ is too low dimensional. We offer some remedy: $p$ is close, in an appropriate sense, to $conv Q$ for some subset $Q$ of size $k$. Similar results hold for Tverberg's theorem as well. This is joint work with Nabil Mustafa."@en . "https://circle.library.ubc.ca/rest/handle/2429/66675?expand=metadata"@en . "27 minutes"@en . "video/mp4"@en . ""@en . "Author affiliation: Alfred Renyi Institute of Mathematics"@en . "10.14288/1.0369719"@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 . "Theorems of Caratheodory and Tverberg with no dimension"@en . "Moving Image"@en . "http://hdl.handle.net/2429/66675"@en .