List of Mathematical Videos
produced by John M. Sullivan

Knot Energies.
Produced at the Geometry Center and the NCSA, 1998. Length 3'20".
Minimizing an energy for knots (motivated by spreading electric charge along the knot) should lead to canonical configurations for each knot or link type. We show experiments with one such energy, whose Möbius invariance is demonstrated with a tour through the conformal group. Minimizing the energy simplifies a complicated unknot to the round circle, and finds nice configurations for other simple links including the trefoil knot and the Borromean rings. Surprisingly, minimization breaks the symmetry of some other torus knots.
The Optiverse, with George Francis and Stuart Levy.
Produced at the NCSA, 1998. Length 6'43".
We present new optimal methods for turning a mathematical sphere inside out. These eversions, computed automatically in Brakke's evolver by minimizing Willmore's elastic bending energy for surfaces, form part of an infinite family with increasing symmetry. Each computation starts from a conformally transformed minimal surface (with twice the symmetry), a critical point for bending energy. The eversions, accompanied by specially composed parambient music, are rendered in varied styles. This highlights the topological events, seen in the changing double-locus of self-intersections.
Knots Minimizing a Möbius-Invariant Energy.
Produced at the Geometry Center, 1993. Length 6'37".
Superseded by Knot Energies, 1998.
Using Max-Flow/Min-Cut to Find Area-Minimizing Surfaces.
Produced at the Geometry Center, 1992.
Published (with written description, pp 107-110) in Computational Crystal Growers Workshop, AMS Selected Lectures in Mathematics, 1992.
Crystalline Approximation: Computing Minimum Surfaces via Maximum Flows.
Produced at the Geometry Center, 1991.
Published (with written description, pp 59-62) in Computing Optimal Geometries, AMS Selected Lectures in Mathematics, 1991.
Computing Soap Films and Crystals, with Fred Almgren, Ken Brakke, Jean Taylor.
Produced at the Geometry Supercomputer Project, 1989. Length 13'50".
Published (with written description by Fred Almgren, pp 3-5) in Computing Optimal Geometries, AMS Selected Lectures in Mathematics, 1991.