- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Proof of a conjecure of Barany, Katchalski and Pach
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Proof of a conjecure of Barany, Katchalski and Pach Naszodi, Marton
Description
B\'ar\'any, Katchalski and Pach proved the following quantitative form of Helly's theorem: If the intersection of a family of convex sets in $\mathbb{R}^d$ is of volume one, then the intersection of some subfamily of at most $2d$ members is of volume at most some constant $v(d)$. They gave the bound $v(d)\leq d^{2d2}$, and conjectured that $v(d)\leq d^{cd}$. We confirmed it. We discuss the proof and further results.
Item Metadata
| Title |
Proof of a conjecure of Barany, Katchalski and Pach
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2016-10-25T09:55
|
| Description |
B\'ar\'any, Katchalski and Pach proved the following quantitative form of
Helly's theorem: If the intersection of a family of convex sets in
$\mathbb{R}^d$ is of volume one, then the intersection of some subfamily of at
most $2d$ members is of volume at most some constant $v(d)$. They gave the
bound $v(d)\leq d^{2d2}$, and conjectured that $v(d)\leq d^{cd}$.
We confirmed it. We discuss the proof and further results.
|
| Extent |
45 minutes
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: Eötvös University
|
| Series | |
| Date Available |
2017-06-07
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0348138
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International