Spectral sequences for multidimensional persistence


Ponente: Andrea Guidolin (Politecnico di Torino)

Lugar: Seminario Mirian Andrés (Edificio CCT)

Hora: lunes 23 de enero, 12:30

Abstract: Persistent homology is a largely used technique in topological data analysis which allows to extract topological information from data. Its success is due to the wide range of situations where it can be applied, from classification of digital images to networks, from biological data to analysis of sensor fields. In short, a filtration of simplicial complexes is constructed from given data, and through the use of homology one obtains a «topological signature» of the data set.

Another mathematical object related to filtrations of simplicial complexes is the spectral sequence, whose relationship with persistent homology has been made clear during the last few years. We consider multidimensional persistence, an n-dimensional generalization of persistent homology, and we introduce a suitable generalization of spectral sequences, explaining the relation between the two concepts and pointing out the advantages of this new approach.

The slides of the talk are available through this link.