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Geometric Analysis Seminar
Seminar information archive ～12/25｜Next seminar｜Future seminars 12/26～
| Organizer(s) | Shouhei Honda, Hokuto Konno, Asuka Takatsu |
|---|---|
| URL | https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/ |
2025/10/08
10:30-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Jinpeng Lu (University of Helsinki)
Quantitative stability of Gel'fand's inverse problem (英語)
https://www.mv.helsinki.fi/home/jinpeng/
Jinpeng Lu (University of Helsinki)
Quantitative stability of Gel'fand's inverse problem (英語)
[ Abstract ]
Inverse problems study the determination of the global structure of a space or coefficients of a system from local measurements of solutions to the system. The problems are originally motivated from imaging sciences, where the goal is to deduce the structure of the inaccessible interior of a body from measurements at the exterior. A fundamental inverse problem, Gel'fand's inverse problem, asks to determine the geometry of a Riemannian manifold from local measurements of the heat kernel. In this talk, I will explain how the unique solvability of the classical Gel'fand's inverse problem can be established on manifolds via Tataru's optimal unique continuation theorem for the wave operator. Next, I will discuss our recent works on the uniqueness and stability of the inverse problem for the Gromov-Hausdorff limits of Riemannian manifolds with bounded sectional curvature. This talk is based on joint works with Y. Kurylev, M. Lassas, and T. Yamaguchi.
[ Reference URL ]Inverse problems study the determination of the global structure of a space or coefficients of a system from local measurements of solutions to the system. The problems are originally motivated from imaging sciences, where the goal is to deduce the structure of the inaccessible interior of a body from measurements at the exterior. A fundamental inverse problem, Gel'fand's inverse problem, asks to determine the geometry of a Riemannian manifold from local measurements of the heat kernel. In this talk, I will explain how the unique solvability of the classical Gel'fand's inverse problem can be established on manifolds via Tataru's optimal unique continuation theorem for the wave operator. Next, I will discuss our recent works on the uniqueness and stability of the inverse problem for the Gromov-Hausdorff limits of Riemannian manifolds with bounded sectional curvature. This talk is based on joint works with Y. Kurylev, M. Lassas, and T. Yamaguchi.
https://www.mv.helsinki.fi/home/jinpeng/
