Gunther Uhlmann studies inverse problems, imaging and partial differential equations. His research asks how measurements made outside an inaccessible region constrain its internal coefficients or geometry. His institutional research account identifies applications to medical imaging and the structure of Earth.[ref]
With Leonid Pestov, he proved a two-dimensional boundary rigidity theorem: for a compact simple Riemannian manifold, boundary distances recover the metric up to a boundary-fixing diffeomorphism. The qualification prevents confusing a recoverable physical geometry with a unique coordinate description.[ref]
This gives a precise version of the imaging question “can travel times reveal the interior?” It also explains why assumptions about ray geometry matter: if measurements never probe a hidden region, changing that region need not change the data.
Gunther Uhlmann, portrait identified on his University of Washington page
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Gunther Uhlmann is a notable physicist known for his contributions to various fields, particularly in the areas of mathematical physics, inverse problems, and differential equations. He has published numerous papers on topics such as scattering theory, quantum mechanics, and the mathematical aspects of imaging and sensing technologies. Uhlmann has been involved in significant academic and research activities, often collaborating with other scientists and researchers.