CHomP

CHomP, Computational homology project. Much of the fascination and challenge of studying nonlinear systems arises from the complicated spatial, temporal and even spatial-temporal behavior they exhibit. On the level of mathematics this complicated behavior can occur at all scales, both in the state space and in parameter space. Somewhat paradoxically, this points to the need for a coherent set of mathematical techniques that is capable of extracting coarse but robust information about the structure of these systems. Furthermore, most of our understanding of specific systems comes from experimental observation or numerical simulations and thus it is important that these techniques be computationally efficient. Algebraic Topology is the classical mathematical tool for the global analysis of nonlinear spaces and functions, within which homology is perhaps the most computable subset. In particular, it provides a well understood framework through which the information hidden in large datasets can be reduced to compact algebraic expressions that provide insight into underlying geometric structures and properties. The material described through these web pages represents our ongoing effort to develop and apply efficient and effective topologically based methods to the analysis of nonlinear systems.


References in zbMATH (referenced in 40 articles )

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  1. Ergür, Alperen A.; Paouris, Grigoris; Rojas, J. Maurice: Probabilistic condition number estimates for real polynomial systems. I: A broader family of distributions (2019)
  2. Barthel, Tobias (ed.); Krause, Henning (ed.); Stojanoska, Vesna (ed.): Mini-workshop: Chromatic phenomena and duality in homotopy theory and representation theory. Abstracts from the mini-workshop held March 4--10, 2018 (2018)
  3. Cucker, Felipe: Grid methods in computational real algebraic (and semialgebraic) geometry (2018)
  4. Cucker, Felipe; Krick, Teresa; Shub, Michael: Computing the homology of real projective sets (2018)
  5. Denham, Graham (ed.); Gaiffi, Giovanni (ed.); Jímenez Rolland, Rita (ed.); Suciu, Alexander I. (ed.): Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018 (2018)
  6. Feragen, Aasa (ed.); Hotz, Thomas (ed.); Huckemann, Stephan (ed.); Miller, Ezra (ed.): Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018 (2018)
  7. Stevenson, Greg: A tour of support theory for triangulated categories through tensor triangular geometry (2018)
  8. Adiprasito, Karim A.; Benedetti, Bruno; Lutz, Frank H.: Extremal examples of collapsible complexes and random discrete Morse theory (2017)
  9. Baake, Michael (ed.); Damanik, David (ed.); Kellendonk, Johannes (ed.); Lenz, Daniel (ed.): Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 (2017)
  10. Friedl, Stefan; Maxim, Laurentiu; Suciu, Alexander I.: Mini-workshop: Interactions between low-dimensional topology and complex algebraic geometry. Abstracts from the mini-workshop held October 22--28, 2017 (2017)
  11. Jaquette, Jonathan; Kramár, Miroslav: On (\varepsilon) approximations of persistence diagrams (2017)
  12. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  13. Bush, Justin; Cowan, Wes; Harker, Shaun; Mischaikow, Konstantin: Conley-Morse databases for the angular dynamics of Newton’s method on the plane (2016)
  14. de Floriani, Leila; Fugacci, Ulderico; Iuricich, Federico: Homological shape analysis through discrete Morse theory (2016)
  15. Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Pilarczyk, Paweł: Inducing a map on homology from a correspondence (2016)
  16. Haro, Àlex; Canadell, Marta; Figueras, Jordi-Lluís; Luque, Alejandro; Mondelo, Josep-Maria: The parameterization method for invariant manifolds. From rigorous results to effective computations (2016)
  17. Krčál, Marek; Pilarczyk, Paweł: Computation of cubical Steenrod squares (2016)
  18. Alexander, Zachary; Bradley, Elizabeth; Meiss, James D.; Sanderson, Nicole F.: Simplicial multivalued maps and the witness complex for dynamical analysis of time series (2015)
  19. Gameiro, Marcio; Hiraoka, Yasuaki; Izumi, Shunsuke; Kramar, Miroslav; Mischaikow, Konstantin; Nanda, Vidit: A topological measurement of protein compressibility (2015)
  20. Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir: Clique topology reveals intrinsic geometric structure in neural correlations (2015)

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