Visualizing Complex Projective Spaces and their Applications

Indiana University, Bloomington IN

Investigators

Abstract

ABSTRACT 0204112 Hanson, Andrew Indiana U Bloomington Complex variables form the basis for virtually every aspect of modern science, and complex projective spaces are the home to the rich world of objects and structures that arise from com-plex variables. Yet attempts to depict geometric aspects of these spaces have been scarce due the prodigious difficulty of higher dimensional visualization and poor understanding of the wealth of relevant problems that touch on complex projective spaces. Modern computer technology provides a number of very significant new tools symbolic manipulation programs, numerical optimiza-tion programs, and interactive computer graphics visualizations that can provide powerful as-sistance for the human mathematical intellect. The benefits of exploiting these tools fall into two major categories: (i) lowering the bar, so to speak, so that a larger number of people, possibly even interested lay persons, can understand the significance and excitement of previously inacces-sible mathematical concepts; and (ii) raising the potential level of research attainment to allow the solution of problems that would be nearly impossible using conventional mathematical research methods.