Leonid Pestov is a mathematician associated with inverse problems for waves and geometry. With Gunther Uhlmann, he proved boundary rigidity for compact simple two-dimensional Riemannian manifolds: boundary-to-boundary distances determine the interior metric up to a change of coordinates fixing the boundary.[ref]
The ambiguity is physical as well as mathematical. Relabeling interior points does not change the travel time between labeled boundary points, so no reconstruction using only those times can distinguish the relabeling. The theorem shows that, under its geometric assumptions, this is the entire ambiguity. Pestov's institutional lecture description also concerns reconstructing coefficients of a wave equation from observations, connecting the geometric theorem with travel-time and wave-imaging measurements.[ref]
https://ias.hkust.edu.hk/events/inverse-problems-for-wave-equation-and-imaging. 2017 institutional event record, mathematical identity and lecture abstract
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