Exploring Visualization Methods for Complex Variables

Authors Andrew J. Hanson, Ji-Ping Sha

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Andrew J. Hanson
Ji-Ping Sha

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Andrew J. Hanson and Ji-Ping Sha. Exploring Visualization Methods for Complex Variables. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 90-109, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


Applications of complex variables and related manifolds appear throughout mathematics and science. Here we review a family of basic methods for applying visualization concepts to the study of complex variables and the properties of specific complex manifolds. We begin with an outline of the methods we can employ to directly visualize poles and branch cuts as complex functions of one complex variable. $CP^2$ polynomial methods and their higher analogs can then be exploited to produce visualizations of Calabi-Yau spaces such as those modeling the hypothesized hidden dimensions of string theory. Finally, we show how the study of N-boson scattering in dual model/string theory leads to novel cross-ratio-space methods for the treatment of analysis in two or more complex variables.
  • Visualization
  • Complex Manifolds
  • High Dimensions


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