Department of Mathematics
Title : Spherical waves, nodal sets, and thermoacoustic tomography
| Speaker: Mark Agranovsky Affiliation: Bar-Ilan University Time: 3:00 pm Friday, 26 August, 2011 Location: G08, 70 Symonds Street |
Abstract
| The spherical mean operator, integrating functions over spheres, is a classical transform playing an important role in analysis and differential equations. The new interest to this old object arose in mid 90s due to new circle of closely interrelated problems: on one side, in approximation theory (complete systems of spherical waves), PDE and spectral analysis (geometry of nodal sets) and, on the other side (and surprisingly almost at the same time) in applications, namely in thermo-and photoacoustic tomography - new trend in medical diagnostic and imaging. In the context, the spherical mean transform is viewed as a Radon type transform, defined on non-standard complexes of spheres. Main questions in inverse problems, integral geometry and mathematical tomography (injectivity, range description, inversion), addressed to the above transform, lead to interesting and challenging problems on the crossroad of PDE, harmonic analysis and integral geometry. We will describe the progress in the subject in the past one and a half decade or so and discuss questions which still remain open. |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
