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Nori Diagrams and Persistent Homology

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Recently, it was found that there is a remarkable intuitive similarity between studies in theoretical computer science dealing with large data sets on the one hand, and categorical methods of topology and geometry in pure mathematics, on the other. In this article, we treat the key notion of persistency from computer science in the algebraic geometric context involving Nori motivic constructions and related methods. We also discuss model structures for persistent topology.

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Acknowledgements

We thank Jack Morava for suggesting the question of model structures for persistent homology discussed in Sect. 6. The second author is partially supported by NSF grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593, by the FQXi Grant FQXi-RFP-1 804, and by the Perimeter Institute for Theoretical Physics.

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Authors and Affiliations

  1. Max–Planck–Institut für Mathematik, Bonn, Germany

    Yuri I. Manin

  2. California Institute of Technology, Pasadena, USA

    Matilde Marcolli

  3. University of Toronto, Toronto, Canada

    Matilde Marcolli

  4. Perimeter Institute for Theoretical Physics, Waterloo, Canada

    Matilde Marcolli

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  1. Yuri I. Manin
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  2. Matilde Marcolli
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Correspondence to Matilde Marcolli.

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Manin, Y.I., Marcolli, M. Nori Diagrams and Persistent Homology. Math.Comput.Sci. 14, 77–102 (2020). https://doi.org/10.1007/s11786-019-00422-7

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