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Persistent topology and applications

This team initiated the branch of topology now called "Persistent Homology" (and more generally "Persistent Topology") as the theory of Size Functions, geometric-topological shape descriptors. Persistent Topology studies the features of the sublevel sets of filtering functions f defined on topological spaces X. Theoretical issues are: the relationship with the "natural pseudodistance" between pairs (X,f), effective computation of "persistence diagrams", 1D reduction of the case of filtering functions with multidimensional range, invariance under certain homeomorphism groups. Current applications are: shape analysis, classification and retrieval, in particular for shapes of natural origin.
The group is active within the Applied and Computational Algebraic Topology Project of the ESF.

Group members

Massimo Ferri

Patrizio Frosini

Barbara Di Fabio

Research partners

Claudia Landi University of Modena and Reggio Emilia (Italy)

Andrea Cerri CNR-IMATI Genova Section (Italy)

Michela Spagnuolo CNR-IMATI Genova Section (Italy)

Andreas Holzinger Medical University and Technical University Graz (Austria)

Tomasz Kaczynski University of Sherbrooke (Quebec, Canada)

Marian Mrozek Jagiellonian University, Krákow (Poland)

Neža Mramor Kosta University of Ljubljana (Slovenia)

Ulrich Bauer Institute for Science and Technology (Austria)

Facundo Mémoli Ohio State University (USA)