ARTIST BIO

David Bachman is a professor at Pitzer College in Claremont, CA. He received a PhD in mathematics in 1999 from the University of Texas at Austin, and has since published over 20 research articles, three books, and received two grants from the National Science Foundation. Ten years ago David's background in mathematics and his affinity for working with his hands converged when he began to experiment with 3D printing. Since then he has created unique two and three-dimensional pieces by using several CAD modeling packages (most notably, Rhino 3D and Grasshopper), a variety of laser cutters, 3D printers, pen plotters, and a garage full of tools. 

ARTIST STATEMENT

The universe may be finite. If true, then if you travel in a spaceship in one direction long enough you’ll eventually return to your start, analogous to what happens when traveling along the surface of the Earth. Such a finite universe has many possible shapes, and each possibility is called a 3-manifold. 

The set off all infinite rays emanating from some origin point in a 3-manifold forms a sphere, like the circle of the horizon when looking around you from a point on the surface of the Earth. This is called the sphere at infinity. 

Some 3-manifolds contain special surfaces (analogous to the equator on a sphere). A ray emanating from the origin point can be colored according to how often it intersects such a surface. In this way, we can assign a color to each point of the sphere at infinity to obtain a cohomology fractal. 

Cohomology Fractal s776 (2019) shows a piece of the sphere at infinity for the 3-manifold s776. This work is derived from an image generated from joint work with Henry Segerman and Saul Schleimer. 

For each knot you can tie, there is an associated 3-manifold. These particular kinds of 3-manifolds have special surfaces coming from the shape of a soap film that spans the knot. Lifting the Figure Eight Knot (2018) simultaneously shows the cohomology fractal on the sphere at infinity coming from the spanning surface for the ``figure eight knot," as well as the surface itself inside of the sphere at infinity. This piece is based on joint work with Henry Segerman