Research

During graduate school at Indiana University, I studied triply periodic minimal surfaces with my advisor, Matthias Weber. My dissertation was centered on finding deformations of these surfaces. In particular, I proved that two minimal surfaces (the gyroid and the lidinoid) admit deformations. In the meantime, check out the Indiana University Virtual Minimal Surface Museum for tons of great pictures. (Click on "Archive".)

The gyroid is a triply periodic minimal surface that contains no straight lines or planar symmetry curvers. It was discovered by Alan Schoen in 1970 and was proven embedded by Grosse-Brauckman and Wohlgemuth (1995). The lack of symmmetries make the gyroid hard to visualize -- I think that the best way to understand it is to look at a rotatable 3-D model (or maybe to have a sculpture in your office). The gyroid has a host of physical applications, among them understanding ketchup, materials science, and modeling the microstructures of cells.

Papers / Publications

Computer imaging

Master's theses

Talks

  • Slides from an invited talk to the St. Mary's College of Maryland MRS (mathematical research seminar) (March 2010 (50 mb file)
  • Slides from an invited talk to the St. Mary's College of Maryland math club (March 2010) (50 mb file)
  • Slides from Mathfest 2009 in Portland, OR (August 2009)
  • Slides from the AMS Central Section Meeting in Bloomington, IN (April 2008)
  • Slides from the AMS/MAA Joint Meetings in San Diego (January 2008)
  • Slides from the Illinois State Mathematics Association of America (ISMAA) 2007 meeting (March 30, 2007)
  • Slides from the AMS/MAA Joint Meetings in New Orleans (January 2007)
  • Slides from the job-talk I gave at Southern Illinois University Edwardsville (March 7, 2006)
  • Slides from a rather low-key talk I gave at the very hospitable Lenoir-Rhyne College (Februrary 9, 2006)
  • Slides from the Eastern Illinois University Colloquium (January 20, 2006)


  • I create my slides using Beamer, a package for LaTeX. You can download a sample LaTeX file for these talks (with no pictures).

Relevant Minimal Surfaces Links

Other Mathematics Links