- Semidefinite programming. For the last ten years, I've been working on a code that solves problems in semidefinite programming. This open source software package, called CSDP, uses a primal-dual interior point method. It has been used by researchers in many disciplines. Along with my former student Joseph Young, I've modified the code to run in parallel on shared memory systems using OpenMP. One student project would be to extend the software by incorporating a sparse Cholesky factorization routine. A somewhat larger project or possible thesis topic would be implementing a first order algorithm for solving very large SDP problems.
- Maximum Independent Set Problems. The maximum independent set problem is an extremely difficult (NP-Hard) combinatorial optimization problem. However, it is possible to use semidefinite programming to obtain bounds on the size of the MIS. Together with former students Richard Hahn and Aaron Wilson, I've developed an SDP based branch and bound code for the solution of MIS problems and used it to solve some problems that have never been solved by other approaches. A possible student project in this area would be the development of a parallelized version of the code that would run on a distributed memory cluster (e.g. a Beowulf.)
- Cosmogenic Nuclide Dating. In an NSF funded project called CRONUS, a group of researchers at several universities is working to improve the accuracy of exposure age dating of samples from measurements of rare isotopes that are produced by cosmic rays that begin to bombard rock after it is exposed on the surface. My part of the project is the calibration of production rates from independently dated samples. I'm currently working with a student, Robert Aumer, who is developing a code for aging depth profile samples.
- Remote sensing of soil moisture. I'm currently working with Jan Hendrickx and his students in the hydrology department on analysis of remote sensing data with applications to hydrology and soil science. In one project, we're using an algorithm called SEBAL to estimate root zone soil moisture from LANDSAT and MODIS images. Several current and former students have been involved in the development of our MATLAB code for soil moisture estimation. We've also investigated the use of radar images for estimation of soil moisture. This research has also included an investigation of the spatial variability of soil moisture at scales ranging from 30m to tens of kilometers and methods for up and downscaling images at different scales.
- Landmine detection. I've also done work with Jan Hendrickx and his students in the hydrology program on modeling the effects of soil physical properties on landmine detection sensors. This project has largely wound down.

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