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Nori Diagrams and Persistent Homology

  • Yuri I. Manin
  • Matilde MarcolliEmail author
Article
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Abstract

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.

Keywords

Persistent homology Nori diagrams Nori motives Thin categories Model structures 

Mathematics Subject Classification

68P15 18B20 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Max–Planck–Institut für MathematikBonnGermany
  2. 2.California Institute of TechnologyPasadenaUSA
  3. 3.University of TorontoTorontoCanada
  4. 4.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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