Preface This conference covered a variety of topics in inverse problems: inverse scattering problems on the line inverse problems in higher dimensions inverse conductivity problems and numerical methods. In addition, problems from statistical physics were covered, including monodromy problems, quantum inverse scattering, and the Bethe ansatz. One of the aims of the conference was to bring together researchers in a variety of areas of inverse problems. All of these areas have seen intensive activity in recent years. Inverse conductivity problems This class of problems was discussed by David Isaacson and Margaret Cheney of Renssalaer Polytechnic Institute and by Gunther Uhlmann of the University of Wash- ington. Uhlmann discussed his work with John Sylvester on the problem of determin- ing anisotropic conductivities in a region from measurements made on the boundary. These measurements may include the Dirichlet-Neumann map or knowledge of the geodesics. Margaret Cheney discussed various algorithms for reconstructing the con- ductivities from the data: these included iterative methods, and Calderon's methods. David Isaacson discussed experimental work being carried out at Renssalaer Poly- technic Institute and ended his talk with an intriguing videotape of actual inverse imaging experiments on a human subject (himself). Adrian Nachman, of the University of Rochester, gave an overview of inverse scattering and conductivity problems. Joyce McLaughlin, of Renssalaer Polytech- nic Institute, presented recent results on inverse spectral problems for second order differential operators. Numerical methods Vladimir Rokhlin of Yale University described a numerical algorithm for inverse scattering based on a Riccati equation for the impedence function combined with cer- tain trace formulae for the unknown functions. Numerical experiments performed in one dimension have shown themselves to be stable, rigorous, and extremely efficient. He hopes to be able to extend the methods to two and three dimensional problems. Soliton problems One dimensional inverse scattering methods are a fundamental tool in the theory of completely integrable systems. Percy Deift of the Courant Institute opened the xi
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