Matt Rathbun

Assistant Professor

Mathematics

California State University, Fullerton

Department of Mathematics

McCarthy Hall 160B

mrathbun(at)fullerton(dot)edu

Office phone: 657-278-7697

Research:

I study Knot Theory and 3-manifolds.

My research involves fibered knots, plumbing operations, Seifert surfaces, unknotting tunnels, Heegaard splittings, and applied knot theory to model DNA-protein interactions.

A knot is exactly what you would think - take a piece of string and tie it up. Only, instead of leaving the ends free, fuse them together, so that you cannot undo the knot. Easy to describe. But the same knot can take on many configurations in space, and things become complicated quite quickly. Suppose I tie two knots, behind my back, hand them to you, and ask you to decide whether they are the same, or different. You will soon find that fancifully trying to rearrange them to look identical is not efficient, or even guaranteed to provide an answer. We need a more systematic way of analyzing these objects.

One rich method of studying knots is thinking about the space around the knot, but excluding the knot itself. This is but one example of a 3-manfiold. A 3-manifold "looks" like ordinary three-dimensional space, but more interesting phenomena can occur. For instance, every lasso can be tightened in ordinary space. But if you exclude a knot from space, then a lasso going around that knot would get "caught", and could not tighten any further. There are even three-manifolds where if you traveled in a rocketship in a straight line for long enough, you would eventually return right to your starting point, but as a mirror image of yourself!

These topics are fascinating, and fun, and also have applications for understanding the configurations of our DNA!

Papers:

I am working on several projects with Ken Baker, Jessica Banks , Dorothy Buck, Marion Moore Campisi, Alexander Coward, Nicholas Jackson, Colin Johnson, Kai Ishihara, Koya Shimokawa , and Mike Williams.

Teaching:

  • Math 414 - Topology - Fall, 2015
  • Math 150A - Calculus I - Fall, 2015
  • Previously Taught:

    Outreach