My first paper (from my dissertation) is on Hausdorff Distances and Convex Sets. I showed that in a normed space, the Hausdorff distance between two bounded, convex sets is the same as the Hausdorff Distance between the boundaries of those sets, and explain why convexity is crucial. I submitted this paper for publication on Monday 1st November, 2004 to the Journal of Convex Analysis. It was published in early 2007.
Another paper from my dissertation is on extending the notion of a spectral scale (as defined by C. Akemann, J. Anderson, and N. Weaver) to the unbounded situation. The focus of this paper is on the single variable case although the multi-variable case is also considered. The paper was submitted in May 2010 and published in the International Journal of Mathematics and Mathematical Sciences in July 2010. The link to the paper is here: http://www.hindawi.com/journals/ijmms/2010/713563.html
I have edited and extended some results on extreme points (the buzzphrase is theorems of Lyapunov type) by Doug Baker before his untimely passing. The paper was submitted to the Journal of Convex Analysis in September 2008 and accepted for publication in July 2009 and was published in spring 2010. The link to the paper is here (a subscription is required): http://www.heldermann.de/JCA/JCA17/jca17.htm#jca172
Doug also did some work on automatic convexity. I do not know how much is original and what, if any of it, should be published. Finding out is my next project.
Mike Cocos has a proposal for a joint paper extending my results on Hausdorff distances to manifolds in some way. It seems worth pursuing. This will be something for us to work on through the coming academic years.
I advanced to candidacy in July 2004. My candidacy talk was a very early draft of my dissertation. An abstract can be found in my research statement as well as in the introduction to the advancement notes. A copy of my advancement notes is available here.
An important element in my dissertation is the notion of non-commutative integration, as investigated by E. Nelson, H. Dye, and I. Segal. On October 11th, 2004, I gave a talk in the graduate student seminar about non-commutative integration. The notes for this talk may be found here.
I finished my dissertation in May 2005 and it has been filed. The abstract for my dissertation is here.