Dr. Seth Oppenheimer
Professor of Mathematics
Director, Undergraduate Research Program, Shackouls Honors College
Research interests: Partial differential equations, applied functional analysis, ordinary differential equations, mathematical modeling.
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I have always worked on problems I have found fun and interesting. My main interest is interdisciplinary mathematical modeling with a whole problem approach. That is, I work with experimentalists in engineering and science to develop models of the particular phenomena they are interested in and use the tools of mathematical analysis to determine answers to questions such as whether the model is well-posed and whether it has the qualitative properties seen in experiment. I proceed to use experimental data to solve the necessary inverse problems to calibrate the model. Finally, using the model predictions I suggest directions for future experimentation. Often such problems raise novel mathematical questions which I then investigate. This has played out in a variety of situations and applied disciplines. Sometimes I end up with a science paper and a related mathematical paper, sometimes just a science paper, and sometimes I work for a while and can show an investigator that what he or she thinks is going on cannot possibly be going on. My training is in applied functional analysis and partial differential equations, though I have built and analyzed models using ordinary differential equations, difference equations, integro-differential equations, and mixed systems of the above. In much of my work, I find doing numerical experiments useful.
Degree: Ph.D. in Mathematics, 1987,
Department of Mathematics, University of Texas at Austin