Summer School in Inverse Problems; June 2009; Newark, DE

University Of Delaware, Newark DE

Investigators

Abstract

Luke DMS-0852454 For the Institute for Mathematics and its Applications (IMA) and its Participating Institutions (PI), the principal investigator and his colleagues organize the IMA/PI Summer School on the Mathematics of Inverse Problems, June 15-July 3. In this project the investigators include students who are not from the participating institutions. The program is geared toward graduate students in the mathematical sciences. The 2009 summer program on the mathematics of inverse problems covers three different themes: inverse problems for hyperbolic partial differential equations, inverse scattering in the frequency domain, and variational techniques for inverse problems. The program covers the techniques used to tackle problems at the cutting edge of mathematical research in each of these areas. Week-long lectures and problem-solving sessions are presented in an informal environment by world leaders in each of these areas -- William Symes (inverse problems for waves), John Sylvester (inverse scattering), and Jonathan Borwein (variational analysis). Two of the three lecture series (inverse scattering and variational techniques) are under contract to appear as separate chapters in a book to be published by Springer in 2010. Inverse problems are everywhere, from determining the causes of global warming, to finding oil and natural gas under the earth's surface, to diagnosing diseases with medical imaging. The basic idea of an inverse problem is simple: given an observation, determine the cause. Unfortunately, most inverse problems are not easily solved: the model for the observation is often incomplete or incorrect, and, even if the model is a perfect match to the truth, it may be impossible to accurately determine the cause from an observation (the curse of so-called "ill-posedness"). The last 20 years has seen a dramatic shift in the mathematics of inverse problems and the capabilities for solving them, initiated largely by improvements in computing power and the concurrent evolution of what is often called "experimental mathematics." Never before have new theoretical tools been able to be tested with such immediacy and practical import. This IMA/PI Summer School on the Mathematics of Inverse Problems aims at preparing future mathematicians for research in this growing and increasingly vital field. The schools bring students together with outstanding researchers in an intensive setting that is intended to lead students from the more familiar course-oriented problem solving skills to the frontiers of mathematical research. Students gain experience not only in attacking problems on advanced and research-grade topics, but also in working collaboratively with people from different backgrounds. The 2009 program has received 51 applications from a diverse group of individuals, 29 from participating IMA institutions and 22 from non-IMA institutions. This project supports students from non-IMA affiliated institutions.