Visualizing the Path from Fermat’s Last Theorem to Calabi-Yau Spaces by Andrew Hanson, PhD

Andrew Hanson, Professor of Computer Science at Indiana University: Abstract: Three decades ago, Alan Barr at CalTech introduced the computer graphics community to an influential modeling technique that created smooth deformations by varying the power of the sphere’s quadratic algebraic equation. These so-called “superquadrics“ eventually found their way into the machine vision community, and were used extensively for modeling and recognition of generic shapes. In 1990, we presented a paper, at the IEEE’s very first Visualization Conference, in which we fancifully toyed with the idea that Fermat’s Last Theorem might have some connection to complexified superquadrics. To support this idea, we developed extensive interactive 4D computer graphics methods to display these bizarre shapes. Our hopes were dashed when Fermat’s theorem was actually proven by Andrew Wiles in 1995. However, the graphical images motivated by complexified superquadrics rose from the ashes of Fermat&