Non UBC
DSpace
Bárány, Imre
2018-08-06T05:02:18Z
2018-02-06T10:36
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.
https://circle.library.ubc.ca/rest/handle/2429/66675?expand=metadata
27 minutes
video/mp4
Author affiliation: Alfred Renyi Institute of Mathematics
Banff (Alta.)
10.14288/1.0369719
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Convex and discrete geometry
Combinatorics
Theorems of Caratheodory and Tverberg with no dimension
Moving Image
http://hdl.handle.net/2429/66675