Four faculty members at the University of Houston plan to run a summer Research Experiences for Undergraduates site. Two topics will be explored each summer. During the first year, E. Dean will supervise two students in research on numerical optimization problems, including a simple model of control of fluid flows, which involves calculating approximate gradients. This topic will have a computational component. S. Ji will lead two students in research in complex geometry by looking at mappings of the unit ball in C2.
Proposed topics for the second summer are rings of operators on inner product spaces, and geometric constructions in matrix spaces; this topic will also have a computational component. Two students will work in this area under the direction of D. Blecher. S, Canic will supervise two students in research on hyperbolic conservation law models and applications, including the use of software packages in computing.
Students will learn to present their ideas orally and in writing, and will interact with all the key faculty and with graduate students and other department faculty and visitors. The topics are suitable for rising seniors and for juniors who have had a course in advanced calculus and either differential equations, complex variables or modern algebra.
A distictive feature of this REU site is the selection of topics, with a focus on analysis, applied analysis and geometry. The faculty who have designed and will supervise the research are all active researchers in these areas.
The key personnel have, among them, some experience in supervising undergraduate research, and experience in mentoring of undergraduates and of women and underrepresented minority students. As well as advertising nationally for students, the group proposes to recruit extensively in Texas, especially in minority-majority colleges, to obtain a good mix of talented student participants.
