Research

Differential geometry, in one form or another, has been my primary research interest. I use techniques of real analysis, complex variable theory, and Kahler geometry. Here I have decided to present my research in annotated bibliography form. As a public facing webpage, this is not meant to be a professional advertisement, but a summary of my activities that is as readable and public-friendly as possible. Enjoy!

Selected publications and preprints

  • “Convergence of compact Ricci solitons” pdf
  • “The Achilles Heel of O(3,1)?” pdf
    William Floyd, Brian Weber & Jeffrey Weeks
    Experimental Mathematics Vol. 11 , Iss. 1, 2002

    Computers routinely use matrices in SO(3) (or E(3)) to process motions in Euclidean space. But what if we want to process motions in hyperbolic space? Unfortunately in that case, floating point errors build up rapidly. When computers manipulate metrics in O(3,1), floating point errors build up exponentially—this is the Achilles heel of O(3,1)—whereas in SO(3) errors only build up arithmetically. Myself and coauthors Bill Floyd and Jeff Weeks discovered that processing in SL(2,C) rather than O(3,1) reduces the exponential constant of the error buildup by half—a huge improvement. Achilles was, in part, the culmination of my senior thesis work at Virginia Tech.