Claremont, Calif. (June 4, 2012) — Pitzer College Associate Professor of Mathematics David Bachman has been awarded a National Science Foundation (NSF) grant to fund research exploring surprising connections between the shapes of soap films and the shape of the universe. The $136,983 award will support Bachman’s project “Applications of Topologically Minimal Surfaces” through August 2015.
Similar to surveyors who centuries ago determined the shape of the Earth, Bachman is hunting for mathematical techniques to determine the shape of the universe.
“Einstein told us that the universe has some shape to it,” Bachman said. “Physicists ask, among all of the possible shapes for the universe, which one do we actually live in? Mathematicians ask, what are the qualitative properties of each of these possible shapes?”
One example of a qualitative property of a given possible shape for the universe is the set of “interesting” surfaces that it contains. In a paper published two years ago, Bachman promoted the idea of studying “topologically minimal” surfaces which are the analogue of “geometrically minimal” surfaces, such as the soapy film stretched across the loop of a bubble-blower wand. Theoretically, topologically minimal surfaces have all of the same properties as geometrically minimal surfaces. The goal of Bachman’s research is to find all properties that are shared by these two kinds of surfaces and relate them to possible shapes of our universe. By focusing on this very specific topic, Bachman hopes to help unveil a very big picture.
“The equator has a certain shape and from that we can extract information about the shape of the Earth,” Bachman said. “Different possible universes have something akin to an equator. From those, I’m trying to extract the possible shapes for the whole universe.”
Bachman previously received a grant from the NSF for a related research project titled “Topologically Minimal Surfaces in 3-manifolds.” The NSF is an independent US government agency responsible for promoting science and engineering through research programs and education.
Professor David Bachman’s website
The National Science Foundation website