Since 2001, I have been collaborating with a series of undergraduate students. For the most part, the focus of the research is knot theory.
My papers with undergraduates can be found at The Online Journal of Undergraduate Papers in Knot Theory.
As part of the MAA's NREUP programme and with funding from the NSF, NSA, and Moody's I offered a summer research programme in knot theory for students from groups underrepresented in mathematics in 2003, 2004, 2005, and 2006.
Since 2004, CSU, Chico has been an NSF REUT site (i.e., joint Research Experiences for Undergraduates and Research Experience for Teachers). Click here for further information.
Here's a java application, PolygonViewer, that Rebecca wrote as part of her project.