A Ph.D. in mathematics (University of Oregon [math.uoregon.edu]) studying functional analysis and operator theory in Banach algebras seems distant from statistical analysis of biomedical data. However, many biomedical questions---motivated by new technologies and computing power---are now appropriately posed in the form of operators and so these concepts have increasing relevance to biomedical data analysis. Most relevant is spectral theory (the mathematics of “inverse” problems), which aims to summarize the characteristics of complex (typically linear) systems. Special cases of this include topics such as principal component analysis and the eigenvalues/vectors for systems described by matrices. Other past projects involved control theory (dynamical systems models having an input term that controls the behavior of the system) and semigroups of operators, whose spectral properties help to characterize the behavior of controlled systems.
An NIH career-transition grant (K25) brought me from my position as Associate Professor of Mathematics at the University of Missouri in Rolla, MO (now Missouri University of Science and Technology [www.mst.edu]) to the University of Washington [www.biostat.washington.edu] and the Fred Hutch. A variety of collaborations at the Fred Hutch, UW and Indiana University have defined the focus of my current efforts on statistical and machine-learning methods for the analysis of microbiome, neuroimaging, metabolomic and genomic data.
Please see Dr. Randolph's CV