String Theory and its generalizations are the best candidates for a truly unified theory of all forces so far. These theories assume one-dimensional 'strings' to be the fundamental building blocks of nature, and, to be consistent, require 10 or more dimensions. One method to otain a physical theory in 4 dimensions (3 space dimensions plus time) is to 'compactify' the extra dimensions. The most studied string compactification is probably heterotic string theory compactified on a Calabi-Yau space in six-dimensions (or three complex dimensions). In 1990, together with P. Candelas (now at Oxford University), we constructed a class of Calabi-Yau manifolds which showed a surprising symmetry- now called mirror-symmetry- between the numbers of particles and anti-particles. Mirror symmetry since has played a crucial role in understanding the nature of string theory and has been generalized to other classes of manifolds and other theories.
Our current project uses methods from arithmetic geometry to understand a long-standing problem in string theory concerning a direct relation between rational conformal field theories and Calabi-Yau manifolds. This is in part motivated by the fact that mirror symmetry is understood best in the context of conformal field theory.
In particular, we compute the Hasse-Weil L-function for simple Calabi-Yau manifolds and attempt to provide a string theoretic interpretation.
Selected publications
I spent a year at Fermilab between 2002-2003 and, as part of the Notre Dame High Energy Elementary Particle Physics Group, I am now a member of the D0 collaboration . While at Fermilab, I was involved in the alignment of the Forward Preshower detector with the Central Fiber Tracker. The Notre Dame High Energy group manages the operation of the Central Fiber Tracker for D0, directs the offline track reconstruction effort for the experiment, and is involved in the building of an improved level-1 track trigger processor for enhanced detector performance at increased luminosity. Although I did not have time to get actively involved in the physics analysis, my physics interests include searches for physics beyond the "standard model", for example the search for evidence of large extra dimensions and signs of supersymmetry. Interested IUSB students have the opportunity to participate in this exciting endeavor to understand the world at the smallest scale by helping with software development, data taking, or analysis.
Recent D0 results can be found here.