
Professional Homepage
Welcome! My mathematical research is in 4dimensional gauge theory and exotic 4manifolds, ChernSimons theory, and symplectic CalabiYau 6manifolds. In education I am known for a pair of textbooks for prospective elementary and middle school teachers.
Here is my most recent
curriculum vitae.
News:
 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
http://code.google.com/p/cubeknots/
Check back soon for code to work with hypercube diagrams.
 Elementary Mathematics for Teachers and Geometry for Teachers,
two books I cowrote with Thomas Parker of MSU, are available at
Singaporemath.com.
You can find instructor resources at:
www.elementarymathforteachers.com

