Descriptive topology is an applied, geometrical discipline for exploring the design and production of pedagogically apt examples in the currently prominent area of low dimensional topology. The mathematics of low dimensions: curved lines, surfaces and spaces, is, to a large part, accessible to direct visualization. This new research tool and its associated practical art, {\em topological design}, draws on the classical fields of differential topology, topological analysis, algebraic geometry, and computer graphics. It promises to gain currency as its foundations become better defined and its principles properly formulated.
Prof. Francis is a member of SIAM and ACM Siggraph. He received his BSmcl from Notre Dame in 1958, an AM from Harvard in 1960, and the PhD in mathematics from the University of Michigan in 1967. We was a Woodrow Wilson Fellow in 1959, and a Lloyd Postdoctoral Fellow in 1968.
Five recent publications.
The Etrucan Venus. in P. Concus et. al. ed., Geometric Analysis and Computer Graphics. Springer-Verlag, New York, 1991.
with Andrew Hanson, and Tamara Munzner. Interactive methods for visualizable geometry. Computer, IEEE Computer Society, V.27, N.7 (1994), 73-83.
with Louis Kauffman. Air on the Dirac Strings. In W. Abikoff, J. Birman, and K. Kuiken, eds. The Mathematical Legacy of Wilhelm Magnus. Contemporary Mathematics, V.169, Amer. Math. Soc., Providence, RI. 1994.
The Hypergraphics Honors Seminar at Illinois. In D. Thomas, ed.. Scientific Visualization in Mathematics and Science Teaching. Assoc. Adv. Comp. in Educ., Charlottville, VA, 1995.
with John M. Sullivan, Robert B. Kusner, Kenneth A. Brakke, Chris Hartman and Glenn Chappell. The Minimax Sphere Eversion. In Konrad Polthier and Hans-Christian Hege, eds., Mathematics and Visualization. Springer Verlag, Berlin, 1997.
Five additional relevant works.
A Topological Picturebook. Springer-Verlag, New York 1987. Translated into Russian and Japanese.
with Donna Cox, Ray Idaszak. The Etruscan Venus. 3.5' narrated videotape in SIGGRAPH Video Review No.49, T. DeFanti and M. Brown, editors, Assoc. Comp. Machinery 6 (1989).
with Daniel Sandin, Louis Kauffman, Chris Hartman, Glenn Chappell. Air on the Dirac Strings. 2.0' narrated videotape in Electronic Theater, SIGGRAPH'93.
with Chris Hartman, Glenn Chappell, Ulrike Axen, Paul McCreary, Alma Arias. Post-Euclidean Walkabout. Virtual Reality Room, SIGGRAPH'94.
with John Sullivan, Ken Brakke, Rob Kusner, Dennis Roseman, Alex Bourd, Chris Hartman, Glenn Chappell, Jason Rubenstein. Laterna matheMagica: a 4-D Stereopticon. GII Testbed, Supercomputing'95.