This Pan-American Advanced Studies Institutes (PASI) award, jointly supported by the NSF and the Department of Energy (DOE), will take place in January 16-27, 2012 at three universities in Chile: the Universidad Técnica Federico Santa María in Valparaiso, the Pontificia Universidad Católica in Santiago, and the Center for Mathematical Modeling of the Universidad de Chile, also in Santiago. Organized by Dr. Gunther Uhlmann of the Department of Mathematics at the University of California-Irvine, California, the institute will focus on leading edge techniques used in the study of inverse coefficient problems and control problems for partial differential equations (PDE). Inverse Problems and PDE control have significant impacts on applied science and engineering including applications to stabilization, identification and design of physical systems (e.g. quantum control), image processing, mathematical finance, astronomy, geosciences, medical imaging and non-destructive evaluation of materials, among others.

This PASI will introduce students to many important techniques in the above subjects. In addition to the exposure and mentoring of young scientists to state-of-the-art methods in inverse problems and PDE control, this PASI will foster international collaboration among researchers from the US and different countries in the Americas. Further, cross-disciplinary efforts will be encouraged between scientists and mathematicians both from the U.S. and abroad. The results from the PASI will be disseminated through a website where all the lectures will be available for downloading.

Project Report

. The PASI was held, January 16-27, 2012, at the Pontificia Universidad Catolica de Chile. The interaction between Control and Inverse Problems (IP) has produced remarkable developments. One of the goals of the PASI was to bring many of these developments to advanced graduate students, posrdocs and other scientists in the Americas interested in these fields and their applications. Another important objective of the PASI was to foster international cooperation throughout the Americas by bringing different areas of expertise in Control and IP in one event. There were approximately 120 participants in this unique Institute from several countries of the Americas and some from Europe. The grant supported about 26 participants from the US and 14 from other countries in the Americas. The remaining participants were supported by the Pontificia Universidad Cat'olica de Chile, Centro de Modelamiento Matematico de la Universidad de Chile, Universidad Tecnica Federico Santa Mar'ia and institutions from France, Finland and other countries. This was a very successful Institute and these goals were achieved. During the first week of the PASI there were a series of minicourses to introduce basic topics in Control and IP to graduate students and postdocs. During the second week there was a workshop that focused on recent developments in the interaction between Control and IP. IP are those where causes for an observed effect are to be determined. In other words, from external observations of a hidden, black box system (patient's body, nontransparent industrial object, Earth interior, etc.) one needs to recover the unknown parameters of the system. Such problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a vast variety of of medical as well as other (geophysical, industrial, radar, sonar) imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modeling in the life sciences. Control problems arise from the need to optimize a given performance criterion, e.g., to dampen out undesirable vibrations of a structure, or more generally to obtain a prescribed behaviour.

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University of California Irvine
United States
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