William H. Kruskal Instructor
I'm a Ph.D. in Mathematics from the University of Washington where I worked under the supervision of Gunther Uhlmann. The main topic of my thesis was the analysis of an inverse source problem for the acoustic wave equation in attenuating media, arising from the developing medical imaging technique of thermoacoustic tomography. During those years as a grad student, I also worked in the microlocal characterization of artifacts for two imaging methods, namely, Quantitative Susceptibility Mapping (MRI) and Computerized Tomography.
My research focuses primarily on the theoretical analysis of inverse problems with real applications coming from medical imaging, geophysics, and the industry (e.g. thermoacoustic tomography, X-ray tomography, quantitative susceptibility mapping). I am particularly interested in the study of inverse problems employing tools from PDE's, differential geometry, functional and microlocal analysis. A secondary goal is the implementation of numerical algorithms to complement and help visualize the theoretical findings.
In the last couple of years at the University of Chicago, I have worked in conjunction with Guillaume Bal in the analysis of several models for narrow beams in the highly peaked-forward scattering regime. This analysis has motivated an applied work in collaboration with mathematicians and engineers from two Chilean universities to model, study, and numerically implement an inverse problem arising in Light-Sheet Fluorescence Microscopy Imaging.