Open Collections

Page Metadata

Item Metadata

Title	Interleavings for categories with a flow and the hom-tree lower bound
Creator	Munch, Elizabeth
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-08-09T11:35
Description	The interleaving distance for persistence modules, originally defined by Chazal et al., is arguably the most powerful, generalizable mathematical idea to come out of TDA in the last decade. The categorification of persistence modules and the related interleaving distance provided a plug-and-play system to create new metrics for functors with a poset category domain. In this talk, we will generalize this work even further to give a definition of the interleaving distance for a category with a flow; that is, a category $C$ with a functor $S:\mathbb{R}_{\geq0} \to \mathrm{End}(C)$ which satisfies certain compatibility conditions. From this framework, we can see that many commonly used metrics, such as the Hausdorff distance on sets and the $\ell_\infty$ distance on $\R^n$ are all examples of interleaving distances. The categorical viewpoint gives an immediate construction for a host of stability theorems. Further, a new construction on elements of a category with a flow called a hom-tree provides a lower bound for the interleaving distance. This work is joint with Anastasios Stefanou and Vin de Silva.
Extent	27.0
Subject	Mathematics Algebraic topology Statistics
Geographic Location	Oaxaca (Mexico : State)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: Michigan State University
Series	BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Date Available	2019-03-24
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0377401
URI	http://hdl.handle.net/2429/69159
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

Download

Media

48630-201808091135-Munch_lrv.mp4 [ 82.29MB ]

Metadata

JSON: 48630-1.0377401.json

JSON-LD: 48630-1.0377401-ld.json

RDF/XML (Pretty): 48630-1.0377401-rdf.xml

RDF/JSON: 48630-1.0377401-rdf.json

Turtle: 48630-1.0377401-turtle.txt

N-Triples: 48630-1.0377401-rdf-ntriples.txt

Original Record: 48630-1.0377401-source.json

Citation

48630-1.0377401.ris

Cite

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.

Include Metadata Specify width in pixels (leave blank for auto-width):

                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    

Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:

https://iiif.library.ubc.ca/presentation/dsp.48630.1-0377401/manifest

Comment

Related Items