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 URL: http://www.tgda.osu.edu