I study Knot Theory and 3-manifolds.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.
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.
[preprint available by request]
Pacific Journal of Mathematics, 259-2 (2012), 473--481. DOI 10.2140/pjm.2012.259.473
Journal of Knot Theory and its Ramifications, Vol 21, No 2 (2012)
Involve, a Journal of Mathematics, Vol 4, No 2 (2011), 103--116.
(This is work that resulted from an REU I helped supervise in 2006, sponsored and headed by Moon Duchin.)