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The boundary rigidity problem

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If you have a question about this talk, please contact Nils Prigge.

The boundary rigidity problem asks to recover a Riemannian metric on a manifold (with boundary) from its boundary distance function. In the talk I will give an overview of the history of the problem, culminating in the 2017 breakthrough of Stefanov, Uhlmann and Vasy who resolved the problem for a large class of metrics in dimension 3 and higher. I will then illustrate some of their techniques in the case where the metrics are assumed to lie a in a fixed conformal class. In this case, the problem locally linearises to a (weighted) geodesic X-ray transform, which can be inverted using methods from microlocal analysis.

This talk is part of the Junior Geometry Seminar series.

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