One future goal is expanding the definition of biorthogonal multiresolution analyses outside of L^2, where these families ordinarily belong. My dissertation contains results regarding families of distributions dual to L^2 functions, which is curious theoretically and more useful in applications.
I enjoy analysis in general - particularly approximation theory, measure theory, probability, statistics, functional analysis, Fourier analysis, and harmonic analysis. My dissertation involved wavelet theory.
In the longterm I am fascinated by tomography, various medical applications (e.g. medical imaging, biostatistics, modeling of health-related statistics, and algorithms related to medical devices), information/communication and coding theory, signal/image processing, pattern recognition, and inverse problems.