Abstract: The classical Gel’fand’s inverse problem asks whether a Riemannian manifold is uniquely determined by the knowledge of the heat kernel on any open subset of the manifold. We study this inverse problem in the non-smooth setting in the framework of RCD$(K,N)$ spaces, namely, metric-measure spaces with syntheticRiemannian Ricci curvature bounded below by $K$ and dimension bounded above by $N$. We establish the unique solvability of Gel’fand’s inverse problem for the class of compact RCD$(K,N)$ spaces whose regular set admits $C^1$-Riemannian structure. As an application, we obtain the stability of Gel’fand’s inverse problem in the class of closed Riemannian manifolds with bounded Ricci curvature, diameter and volume bounded from below. We note that the results are new even for Einstein orbifolds  and (weighted) Riemannian manifolds with non-smooth boundary. This is a joint work with Jinpeng Lu (University of Helsinki), based on arXiv:2602.14527.

 

Link Information: Zoom Meeting

https://us02web.zoom.us/j/82651553026?pwd=DvizJ5Q1HfITxCIVyTePH5xBnhuKiU.1

Meeting ID: 826 5155 3026

Passcode: 825813

 

Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chao-Ming Lin (NTU), Wei-Bo Su (NCU), Chung-Jun Tsai (NTU)