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.

  • And this is 9^2_32.
  • A completed tensegrity model by Rusty Wallace.
  • This is an illustration of the structure of self-contacts in a tight link called the Borromean rings.
  • The Alexander basis of a solid in space before and after a diffeomorphism of the body.
  • The Babbage Engine at the British Science Museum.
  • A simple tensegrity.
  • This is me.
  • 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.
  • John Maeda's number butterflies.
  • This link is called 9^2_40.
  • This knot is called 8_6. This tight shape for the knot was found by our software.
  • This is a closeup from Tait's "Ninefold Knottiness"
  • This is 9^2_37.
  • For this link, it's very hard to rule out certain symmetries.
  • 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.
  • Here I am teaching Math 4250.
  • This knot is called the "Chinese Button" knot. This configuration was found by our software Ridgerunner.
  • A detail from an experimental tensegrity construction.
  • My daughter Violet at the Princess Diana playground.
  • This is a painting by Walter Obholzer which I saw at the Massachusett Museum of Contemporary Art.
  • This is 9^2_38.
  • This is an illustration from one of my students of a complicated isotopy demonstrating a symmetry of a link.
  • This is a picture from my current project. It's a sample space describing (abstractly) certain paths contained in a slab.

I live in the beautiful town of Athens, Georgia with my wife Tammy, our daughter Violet, and a small herd of dogs and 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.

During the years 2013-2016, I’ll be teaching Math 2250 (Differential Calculus) in the fall semester and Math 2260 (Integral Calculus) in the spring, with the Math 4500/4510 sequence (Numerical Analysis) thrown in a few times for good measure. For many years, I ran the Geometry VIGRE Group which involves undergraduates and graduate students in a research project. I was honored to receive the Richard B. Russell teaching award in 2007.

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

  • Robot Calculus. I am working on a curriculum to teach first and second semester calculus with demonstrations and problems from robotics. The draft curriculum is completed, with the differential calculus course based on a small robot named Cy which throws a ball about a meter into a coffee cup. The second semester course has some neat 3d-printed manipulatives and includes the Calculus Wars, Episode i^4 educational game.
  • During the year, I volunteer to teach math occasionally to a class of grade 1-3 students at the Waseca Montessori school.
  • I host a small utility to parse Athena class rolls into usable data formats, including CSV, the WebWork classlist format, and the gmail import contacts format.