Broadly speaking, my research interests lie at the intersection of numerical analysis and probability/ statistics. Specifically, I am interested in the areas of Uncertainty Quantification and Compressed Sensing. For my research in Uncertainty Quantification, I am exploring methods for distinguishing and integrating aleatoric and epistemic uncertainties in computational models and systems. In collaboration with Professor Paul Dupuis, we have developed a novel technique to produce robust, meaningful, and computationally feasible bounds on performance measures of interests when the underlying uncertain parameters have both known and unknown distributions. For my work in Compressed Sensing, I am working with Professor Jan Hesthaven and Professor Edward Walsh in applying sparse-gradient l-1 reconstruction techniques for fMRI studies. We have developed a new minimization algorithm to recover fMRI data sets from an extremely low number of Fourier samples. Both these projects have considerable potential for future work in their respective fields.
I also worked at at Raytheon BBN Technologies where we developed a numerical wave propagation model for broadband acoustic sources through realistic atmospheres.
