• Currently a Postdoctoral Fellow in the Department of Mathematics at Colorado State University
  • PhD in Mathematics from University of North Carolina, Chapel Hill
  • BS in Mathematics from University of Colorado Denver
  • I'm from Colorado! (Everyone seems to have Colorado pride nowadays.)
  • Aside from math, I enjoy biking, hiking, website design, making vector graphics, occasionally playing video games, and some other things too.
  • Email:  
  • Spring 2019: Projects in Applied Mathematics (MATH 435)
  • Fall 2018: Introduction to Numerical Analysis (MATH 450)
  • Prior to my postdoctorate, I've taught and written curriculum for a wide range of courses; see my CV for details.
What distinguishes me from other instructors? Where appropriate, I've done the following:
  • Create computer visualizations and interactive demonstrations (see the "Teaching" link above)
  • Bring in real life examples and data, and encourage mathematical modeling of real data
  • Provide historical context to concepts, theorems, algorithms, etc, by assigning problems requiring work with primary sources
These are some of my current and past research interests and projects.
  • Early detection of viral infection with machine learning. The challenge here is to use machine learning tools with omics and timeseries data to get an extremely early signal of the body's response to infection by influenza (or other common respiratory viruses). One facet of this is to identify of infected/infectious individuals before they become symptomatic; it almost goes without saying that being able to do this reliably would have monumental implications for public health. Another facet of this is an inverse problem in some sense - supposing someone is infected, can we infer how long it's been since they were exposed? To answer these questions I analyze a wide variety of data; much of this is so-called "omics" data - microarray and next-generation transcriptomics, proteomics, metabolomics, and so on - using machine learning and sparse optimization tools.
  • Passive tracer problems. My PhD research is on transport of passive scalars in shear flow, working with Roberto Camassa and Rich McLaughlin. The broad research question is essentially, "when a dye gets pushed by a fluid flow in a pipe, what influence does the shape of the pipe have in shaping the dye?" Our approach is to both apply techniques in mathematical analysis to the advection-diffusion equation to gain quantitative predictions at both short and long times, and use numerical simulations for validatation. The short answer is that the cross section does play an important role. We have published papers at both Physical Review Letters and Science covering different aspects of this question.
  • Stability problems. I spent the summer of 2013 at Los Alamos National Lab, working with Balu Nadiga on a stability problem in geophysical fluid dynamics. The broad goal here is to be able to understand the mechanism for, and size of, instabilities in ocean flows. My project was to develop a numerical code for one such scenario.
  • Spectral image segmentation. In my undergraduate, I worked with Andrew Knyazev on a project on spectral image segmentation. The goal is to develop a black-box method for identifying the salient features of an image. I also briefly assisted on a code for optimal polynomial fitting in the sup-norm, that is, finding an optimal n-th degree polynomial to minimize the sup-norm of the error function f(x) - pn(x) on an interval.