"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 .
"Banff (Alta.)"@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 .