My main theoretical interest is in understanding why we are able to do statistics as well as we do on very high dimensional datasets without knowing much, even though least favorable (malicious God) formulations suggest we should not be able to do anything. Currently this has led me to focus on estimation of covariance matrices and their eigenstructures in high dimensions. Parallel applied interests are in:

1.  Computational biology, specifically at the moment regulatory networks in the cell. To my surprise some of the methods flowing out of my primary interest are relevant to this one.
2.  Atmospheric sciences ... in part as a ready source of questions based on very high dimensional data.