Variational analysis and optimization
I am interested in the properties of polynomial root functions and spectral functions, which arise in eigenvalue optimization problems. Examples of spectral functions are the spectral abscissa (largest real part of an eigenvalue) and spectral radius (largest eigenvalue in modulus), which are tied to the asymptotic behavior of dynamical systems. This paper (http://www.sciencedirect.com/science/article/pii/S0362546X11000319) concerns the variational analysis of polynomial root functions and am co-authoring a second on spectral max functions. I am also co-authoring a paper on root activity of the polynomial radius & abscissa at local optima, subject to affine constraints.
Statistics, data visualization applied to public health surveillance
My work in statistics and data visualization revolves around my involvement in a public health project for influenza surveillance. This work consists of three main components: data visualization, identifying patterns of error in data and developing an automated routine for error detection, and generating prediction intervals for the proxy flu rate. I wrote the accrued package in R for visualizing data quality of partially accruing data, which can be found here: http://www.r-project.org/.