David Bachman; Matthias Goerner; Saul Schleimer; Henry Segerman

Statement

David Bachman is a professor at Pitzer College in Claremont, CA. David studies geometry and topology, and enjoys creating 3D sculptures that illustrate these ideas. Matthias Goerner is a software engineer by day and mathematician by night. His mathematical interests include hyperbolic geometry and three-manifolds with a particular focus on computation. Saul Schleimer is a geometric topologist, working at the University of Warwick. His other interests include combinatorial group theory and computation. Henry Segerman is an Associate Professor in the Department of Mathematics at Oklahoma State University. His interests include geometry and topology, 3D printing, virtual reality, and spherical video.

Artworks

Four "views" of the inside of closed hyperbolic three-manifolds. Each three-manifold contains a surface; when a “light ray” leaves your eye it becomes darker when it crosses the surface in the positive sense and lighter when it crosses in the negative sense. The elaborate patterns come from the complicated geometry and topology of the ambient three-manifold. The four manifolds (in reading order) are m280(1,4), s227(6,1), s400(1,3), and s861(3,1) from the SnapPy census. See our paper at https://arxiv.org/abs/2010.05840 for more details.