My first paper is on Hausdorff Distances and Convex Sets. We show 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. We submitted this paper for publication on Monday 1st November, 2004 to the Journal of Convex Analysis. It was published in early 2007.
Another paper will be on extending the notion of a spectral scale (as defined by C. Akemann, J. Anderson, and N. Weaver) to the unbounded situation. At least for now, the focus of this paper is on the single variable case, but we probably will not submit it until we have more material. A preprint of what we have now is available here.
I am also editing and extending some results on automatic convexity and extreme points by Doug Baker before his untimely passing. My initial rewrite of his work is now complete and can be found here. I hope to produce up to two papers from this work.
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 have finished writing my dissertation and it has been filed. The abstract for my dissertation is here.