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Powers of convex bodies Rotem, Liran
Description
Given a convex body $K$ and a real number $a$, how should we define the convex body $K^a$? One way to answer this question is to write down a list of natural properties we expect from such a power, and then prove existence and uniqueness of a construction satisfying these properties. In this talk we will explain why a natural power operation does not exist for $a > 1$, but does exist for $0 < a < 1$. We will also discuss the uniqueness question, which is more delicate. Based on joint work with Vitali Milman.
Item Metadata
Title |
Powers of convex bodies
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-05-22T16:30
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Description |
Given a convex body $K$ and a real number $a$, how should we define the convex body $K^a$? One way to answer this question is to write down a list of natural properties we expect from such a power, and then prove existence and uniqueness of a construction satisfying these properties.
In this talk we will explain why a natural power operation does not exist for $a > 1$, but does exist for $0 < a < 1$. We will also discuss the uniqueness question, which is more delicate.
Based on joint work with Vitali Milman.
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Extent |
30 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Minnesota
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Series | |
Date Available |
2017-11-20
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0358001
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International