A Course/Seminar:
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INVERSE PROBLEMS
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Mehrdad Shahshahani
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Professor of IPM
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Broadly
speaking, Inverse Problems are about obtaining information regarding an object
or phenomenon that is not directly accessible or observable.� Perhaps the most
publicized inverse problem in mathematics is, Can one hear the shape of a
drum?� Inverse problems have a wide range of applications in sciences.� In
medical sciences, there is the problem of interpreting CAT scan, PET, fMRI or
other medical imaging data.� An essential feature of these problems is the
inversion of the Radon Transform.� Understanding the structure of DNA or other
molecules from the X-ray diffraction data are examples of inverse problems.� In
geophysics, the shock waves of an earthquake provide information about the
structure the earth.� In physics there is the problem of the determination of a
potential from the scattering data.
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The purpose of the
course/seminar is to provide the background material for the IPM workshop on
Inverse Problems scheduled for February 2003.� Several distinguished experts are
expected to attend the meeting.� To benefit from the meeting, students are
encouraged to familiarize themselves with the background material so that they
can interact scientifically with the experts at the meeting.
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The course meets once a
week for two hours (tentatively scheduled for Tuesdays at 5 pm, at IPM, Niavaran).�
The syllabus for the course is as follows:
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- Mathematical tools
(Radon transforms, Fourier transforms etc.)
- Reconstruction
algorithms.
- Resolution, accuracy,
ill-posed problems, incomplete data and other practical matters.
- 3-D imaging.
- Scattering and inverse
scattering for the wave equation.
- Physical background and
the formulation of the problem.
- Theories of
Gelfand-Levitan and Marchenko.
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Starting date:
Tuesday, October 29,� 2002
Time: 17:00, every Tuesday
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Place: �School of Mathematics, IPM,
��������� ��Nivaran Sqr.,
���������� �Tehran, Iran.