Welcome! My mathematical research is in 4-dimensional gauge theory and exotic 4-manifolds, Chern-Simons theory, and symplectic Calabi-Yau 6-manifolds. In education I am known for a pair of textbooks for prospective elementary and middle school teachers.
Here is my most recent
- Read my recent paper on embedded knotted tori in R^4 by going to my preprint link above. This paper describes a new way to embed tori into R^4 called a hypercube diagram and shows how that representation can be used to construct useful and computable invariants of the knotted tori.
This paper is a key part of
my work to understand smooth embeddings combinatorially. Earlier work with Adam Lowrance in one dimension lower lead to cube diagrams of knots in R^3, which can also be accessed at the link above.
Here is a picture of a cube knot (thank you Justin Reusch!):
For computer code to visualize and work with cube diagrams, go to
Check back soon for code to work with hypercube diagrams.
- Elementary Mathematics for Teachers and Geometry for Teachers,
two books I co-wrote with Thomas Parker of MSU, are available at
You can find instructor resources at: