Department Receives $2 Million Research Training Grant from NSF

The principal investigators of the Research Training Grant in Inverse Problems and Partial Differential Equations. From left to right: Professors Jim Morrow, Gunther Uhlmann, Tatiana Toro, Robin Graham, and Hart Smith.

The Department has been awarded a five-year Research Training Group (RTG) grant from the National Science Foundation. Funded in part through the American Recovery and Reinvestment Act of 2009, the total budget for the grant is $2,090,940. The RTG grants are one component of an NSF effort to increase the number of well-prepared U.S. citizens, nationals, and permanent residents who pursue careers in the mathematical sciences and other NSF-supported disciplines. They are meant to support the training activities of a group of faculty who have a common research interest. The research area of our grant is Inverse Problems and Partial Differential Equations (IPDE), and the principal investigators are Professors Gunther Uhlmann, Robin Graham, James Morrow, Hart Smith, and Tatiana Toro.

Inverse problems arise in practical situations such as medical imaging, geophysics, and non-destructive evaluation where measurements made at the frontier of a body are used to deduce properties of the inaccessible interior. For example, electrical impedance tomography involves the determination of the conductivity inside a body from knowledge of the currents that result from induced voltage distributions on the surface. In geophysical imaging, intense sound impulses are directed into the earth, and the seismic imaging problem is to determine the physical properties of the subsurface earth from recordings made of the resulting echoes. It is currently the key method for locating deep oil deposits. Each of these problems in turn is mathematically modeled by a partial differential equation, and a key step is to understand how the solutions to those model equations depend on the physical parameters of the medium.

The largest portion of funding in the RTG grant is to provide stipend support for graduate students and postdoctoral researchers. An average of seven graduate students each year will be supported as research assistants, providing time to focus on their thesis research free of teaching duties. The grant will provide partial funding for one or two postdoctoral researchers at any time, with half the teaching load of a standard Acting Assistant Professor.

In addition, the grant will support an array of activities that enhance the recruitment and success rate of students working in areas related to IPDE. A major new activity is a three-week summer school for advanced undergraduate students and beginning graduate students. These students will be selected from applicants across the country, and the summer school will be run in parallel to the highly successful Research Experience for Undergraduates program run by James Morrow. The first Summer School will take place in June of 2010. Two mini-courses will be taught, by Gunther Uhlmann and Hart Smith, on the mathematics of x-ray imaging and signal processing. Guest lecturers will be invited each week, and labs will be run involving computer implementation of the algorithms discussed in the lectures.

The RTG grant will also support the group’s Visiting Academic and Industrial Internship Program, where the Department’s own graduate students make extended visits to other academic departments in the U.S. and abroad and take part in industrial internship programs at research laboratories in the United States. In past years, students in IPDE have carried out internships at Lawrence Livermore National Laboratory and at Chevron Energy Technology Company in California. Students have also paid extended visits to universities across the country, as well as to Novosibirsk and Khanty-Mansiysk, Russia, and Helsinki, Finland.

Finally, RTG funds will support undergraduate research projects on campus in a range of mathematical topics. The involvement of undergraduates in research is a high priority at the University of Washington, and projects from around campus are highlighted at the annual Undergraduate Research Symposium. The number of undergraduate research projects in mathematics has increased substantially during the past decade, owing in part to ten years of support from the VIGRE grant. Some research projects involve working on questions in mathematical theory and applications, while others have brought students into elementary school classrooms to assist teachers in developing their students’ mathematical skills. The RTG grant will maintain our already strong culture of undergraduate involvement in creative math projects.

In all these ways, the RTG grant will provide a substantial enhancement to the Department’s activities for the next several years.

Hart Smith