My work is focused on developing and implementing methods for making decisions under uncertainty. I work in stochastic programming, a subfield of mathematical programming that studies optimal decision-making problems when there is uncertainty present in the form of a probability distribution.

My current research studies a method of using observational and/or simulated data to make decisions in the absence of an explicit probability distribution. This is accomplised through use of the statistical likelihood function in the mathematical program. In addition to developing a solution algorithm, I am also exploring how to quantify the value of additional observations for reducing the uncertainty of the problem and finding better solutions.

I am applying this technique to the problem of the use of water in Tucson. In the desert water is especially scarce, and by studying the most economically efficient way to use it I hope to help us conserve water and protect our future.

A short list of papers published, in preparation, or given as an important part of my graduate work.

A short list of research talks given.

I spent my first three semesters in the Program in Applied Mathematics working with Dr. Jerome Moloney, a professor in Optical Sciences and Mathematics. While there I did work on genetic algorithm optimization and numerical simulation of semiconductor lasers

The Program in Applied Mathematics requires all students to work on three single-semester research projects for their first three semesters in the program. My results over three semesters are given below

  • Third Semester Research Project. Conducted with Dr. Jerome Moloney on numerical simulation of a semiconductor laser cavity. Final Paper, Presentation

    Paper given December 17, 2008, Presentation given on Deceber 11th, 2008

  • Second Semester Research Project. Conducted with Dr. Juan Restrepo on numerical methods for solving inverse problems. Final Paper, Presentation

    Paper given May 13th, 2008, Presentation given on May 16th, 2008

  • Applied Math Lab Research. Done in collaboration with David Lyttle and Rebecca Stockbridge. Focused on observing and describing the motion of single beads of honey down a vertical wire. Final Paper, Presentation

    Paper given November 29th, 2007, Presentation given on December 6th, 2007