Our current collaboration with Michael Kirby of Colorado State University is on extending the Whitney embedding algorithm to give isometric embeddings of digh-dimensional data. We are also working on extending M/NSET (multivariate/nonlinear state estimation technique) to more general situations (e.g., constructing surrogate functions). David Dreisigmeyer also works with Prof. Kirby's grad students using facial illumination effects (via the Grassmann manifold Karcher mean) to improve face recognition. Current research includes:

1. Dealing with hyperspectral data (we're going to apply for a DCI postdoc)
2. Inverse protein design. The protein folding/design problem is a large scale optimization problem. It can be stated as a multidisciplinary design optimization problem where finding derivative information may be prohibitively expensive or impossible. Being able to handle equality constraints is crucial in order to deal with this problem in order to relate the design variables to the system variables.