Welcome to my webpage! I am a professor of mathematics at the University of Georgia, and Associate Head of the Mathematics Department. My research focuses on the shapes of random curves and polygons. I’m particularly interested in questions like How likely is it that a random curve is knotted?, or What can we expect from a random diagram of a random space curve?. My research is in the general area of geometric knot theory. An introduction to the subject is contained in this short course (and part II of the course) which I gave at the ICTP in Trieste, Italy in 2009. I am also interested in the arts, especially in computer graphics and in sculpture.

  • This knot is called the "Chinese Button" knot. This configuration was found by our software Ridgerunner.
  • And this is 9^2_32.
  • This knot is called 8_6. This tight shape for the knot was found by our software.
  • This is an illustration of the structure of self-contacts in a tight link called the Borromean rings.
  • A detail from an experimental tensegrity construction.
  • For this link, it's very hard to rule out certain symmetries.
  • This is 9^2_38.
  • This is a painting by Walter Obholzer which I saw at the Massachusett Museum of Contemporary Art.
  • This is a closeup from Tait's "Ninefold Knottiness"
  • A poster I made for a conference. The lines on the bunny are "geodesics", meaning that they follow shortest paths along the bunny's curved surface.
  • This is an illustration from one of my students of a complicated isotopy demonstrating a symmetry of a link.
  • This is 9^2_37.
  • The Alexander basis of a solid in space before and after a diffeomorphism of the body.
  • A completed tensegrity model by Rusty Wallace.
  • This link is called 9^2_40.
  • A simple tensegrity.
  • The Babbage Engine at the British Science Museum.
  • John Maeda's number butterflies.
  • This picture is a sample space describing (abstractly) certain paths contained in a slab.
  • This is a Sol Le Witt wall drawing. Le Witt's art is all in the form of directions; the actual drawings are always done by someone else.

I live in the beautiful town of Athens, Georgia with my wife Tammy, our daughter Violet, and a small herd of cats that seem to keep wandering in off the streets and not leaving. My daughter seems to really want a lizard. Or a hamster. So maybe we’ll get that soon. We live in a 1953 ranch house that we’re slowly renovating, and at at our current speed we anticipate the renovations will be completed by 2053. (Maybe.) I grew up in the suburbs of Philadelphia, and moved to Georgia by way of Massachusetts in 2000. Before Massachusetts, where I worked at the University of Massachusetts GANG lab, I was a graduate student at the University of Pennsylvania and an undergraduate at Vassar College.

For the next few years, I intend to teach mostly the Differential Geometry of Curves and Surfaces (MATH 4250) course, which I’m gradually rewriting to include more physical models and some aspects of computational and discrete geometry.

My office is Boyd 448. Office phone: 706-542-2595. Email: (my full name) at gmail.com. Mailing address: Jason Cantarella, UGA Mathematics Department, Athens GA 30602.

My cv is available as well as my Google Scholar profile. I’ve contributed a number of math-related models for 3d printing to Thingiverse. Some movies of tightening knots are available on my web page from an old research project.

Current Projects