MATH Seminar

Title: Local and global boundary rigidity
Colloquium: Analysis and Differential Geometry
Speaker: Plamen Stefanov of Purdue University
Contact: Yiran Wang,
Date: 2023-10-27 at 2:00PM
Venue: MSC W301
Download Flyer
The boundary rigidity problem consists of recovering a Riemannian metric in a domain, up to an isometry, from the distance between boundary points. We show that in dimensions three and higher, knowing the distance near a fixed strictly convex boundary point allows us to reconstruct the metric inside the domain near that point, and that this reconstruction is stable. We also prove semi-global and global results under certain an assumption of the existence of a strictly convex foliation. The problem can be reformulated as a recovery of the metric from the arrival times of waves between boundary points; which is known as travel-time tomography. The interest in this problem is motivated by imaging problems in seismology: to recover the sub-surface structure of the Earth given travel-times from the propagation of seismic waves. In oil exploration, the seismic signals are man-made and the problem is local in nature. In particular, we can recover locally the compressional and the shear wave speeds for the elastic Earth model, given local information. The talk is based on joint work with G.Uhlmann (UW-Seattle) and A.Vasy (Stanford). We will also present results for a recovery of a Lorentzian metric from red shifts motivated by the problem of observing cosmic strings. This work was featured in the news section of Nature and got recently a Frontiers of Science Award.

See All Seminars