Author: Dmitriy Morozov

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AUTHOR

Dmitriy Morozov

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European Congress of Mathematics Kraków, 2 – 7 July, 2012

2013

Persistent homology is a recent grandchild of homology that has found use in science and engineering as well as in mathematics. This paper surveys the method as well as the applications, neglecting completeness in favor of highlighting ideas and directions. 2010 Mathematics Subject Classification. Primary 55N99; Secondary 68W30.

GrandchildPersistent homologyMathematics Subject ClassificationScience and engineeringHomology (mathematics)EpistemologySingular homology

researchProduct

PEPhysical Sciences and Engineering
- PE2Fundamental Constituents of Matter
  - PE2_1Theory of fundamental interactions
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  - PE2_3Experimental particle physics with accelerators
  - PE2_4Experimental particle physics without accelerators
  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
  - PE2_9 Electromagnetism
  - PE2_10Atomic, molecular physics
  - PE2_11Ultra-cold atoms and molecules
  - PE2_18Equilibrium and non-equilibrium statistical mechanics: steady states and dynamics
  - PE2_14Lasers, ultra-short lasers and laser physics
  - PE2_17Metrology and measurement
  - PE2_16Non-linear physics
  - PE2_12Optics, non-linear optics and nano-optics
  - PE2_13Quantum optics and quantum information
  - PE2_15Thermodynamics
- PE1Mathematics
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  - PE1_15Generic statistical methodology and modelling
  - PE1_4 Algebraic and complex geometry
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  - PE1_5Lie groups, Lie algebras
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  - PE1_17Mathematical aspects of computer science
  - PE1_3Number theory
- PE3Condensed Matter Physics
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  - PE11_12Semi-conducting and magnetic materials engineering
  - PE11_13Metamaterials engineering
  - PE11_14Computational methods for materials engineering
LSLife Sciences
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- LS2Integrative Biology: from Genes and Genomes to Systems
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SHSocial Sciences and Humanities
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