Exploring Visualization Methods for Complex Variables

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. CP2 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. 1998 ACM Subject Classification I.3.5 Computational Geometry and Object Modeling, J.2 Physical Sciences and Engineering Keywords and phrases Visualization, Complex Manifolds, High Dimensions Digital Object Identifier...

• Type: Conference
• Year: 2010
• Where: DAGSTUHL
• Authors: Andrew J. Hanson, Ji-Ping Sha
• Keywords: Complex Manifolds, Complex Variables, DAGSTUHL 2010, Software Engineering, Specific Complex Manifolds