Topology, Geometry and Data Seminar - Crichton Ogle

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Crichton Ogle
March 28, 2017
4:00PM - 5:00PM
Location
Cockins Hall 240

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Add to Calendar 2017-03-28 16:00:00 2017-03-28 17:00:00 Topology, Geometry and Data Seminar - Crichton Ogle Title: Towards a structure theorem for finite C-modules; a preliminary reportSpeaker: Crichton Ogle (Ohio State University)Abstract: The classification of finite persistence modules results in a decomposition into indecomposable summands, unique up to reordering, from which the bar code representation of that module is derived.The degree to which this classification theorem generalizes is an important open question in topological data analysis. To this end, we observe that if C is the categorical representation of a finite partially ordered set, and F: C -> (vector spaces over k) is a C-module, then F may be decomposed in a similar fashion.However, unlike the 1-dimensional case (corresponding to a finite totally ordered set), one does not necessarily have uniqueness up to reordering. In other words, modules can be decomposed, but in a possibly non-unique fashion.We will discuss the problem of algorithmically finding indecomposable summands, and show how the method gives a reasonable answer in the case of "generic" n-dimensonal persistence modules.Seminar URL: http://www.tgda.osu.edu Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public
Description

Title: Towards a structure theorem for finite C-modules; a preliminary report

Speaker: Crichton Ogle (Ohio State University)

Abstract: The classification of finite persistence modules results in a decomposition into indecomposable summands, unique up to reordering, from which the bar code representation of that module is derived.

The degree to which this classification theorem generalizes is an important open question in topological data analysis. To this end, we observe that if C is the categorical representation of a finite partially ordered set, and F: C -> (vector spaces over k) is a C-module, then F may be decomposed in a similar fashion.

However, unlike the 1-dimensional case (corresponding to a finite totally ordered set), one does not necessarily have uniqueness up to reordering. In other words, modules can be decomposed, but in a possibly non-unique fashion.

We will discuss the problem of algorithmically finding indecomposable summands, and show how the method gives a reasonable answer in the case of "generic" n-dimensonal persistence modules.

Seminar URLhttp://www.tgda.osu.edu

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