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Anna-Laura Sattelberger: Algebraic Aspects of Multiparameter-TDA

Time: Tue 2021-11-09 10.15

Location: KTH, 3721, Lindstedtsvägen 25 and Zoom (meeting ID: 659 3743 5667)

Lecturer: Anna-Laura Sattelberger (MPI Leipzig)

Abstract

Topological data analysis uses persistent homology as a main tool to investigate data. In the one-parameter case, persistence modules naturally are graded modules over the univariate polynomial ring and hence perfectly understood from an algebraic point of view. One associates the so-called barcode, from which one reads topological features of the data.

Generalizing persistent homology to a multivariate setting allows for the extraction of finer information of the data. Its algebraic properties are more subtle. In this talk, I give insights into an ongoing project with René Corbet and Wojciech Chachólski in which we study multipersistence modules. We introduce the shift-dimension. This is a new, stable invariant of multipersistence modules obtained as the hierarchical stabilization of a classical invariant.

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Belongs to: Department of Mathematics
Last changed: Oct 11, 2021