BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Plamen Stefanov (Purdue University West Lafayette\, USA.) DTSTART:20201103T150000Z DTEND:20201103T160000Z DTSTAMP:20260423T005741Z UID:WOPARA/13 DESCRIPTION:Title: Local and global boundary rigidity\nby Plamen Stefanov (Purdue Univers ity West Lafayette\, USA.) as part of Webinar on PDE and related areas\n\n \nAbstract\nThe boundary rigidity problem consist of recovering a Riemanni an metric in a domain\, up to an isometry\, from the distance b etween boundary points. We show that in dimensions three and hig her\, knowing the distance near a fixed strictly convex boundary point allows us to reconstruct the metric inside the domain near that point\, an d that this reconstruction is stable. We also prove semi-global and g lobal results under certain an assumption of the existence of a strictly convex foliation. The problem can be reformulated asa r ecovery of the metric from the arrival times of waves between b oundary points\; which is known as travel-time tomography. The interest i n 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 innature. In particular\, we can r ecover locally the compressional and the shearwave speeds for the elastic Earth model\, given local information. The talk is based on joint work w ith G.Uhlmann (UW) and A.Vasy (Stanford). We will alsopresent results for a recovery of a Lorentzian metric from red shifts motivatedby the problem of observing cosmic strings.\n LOCATION:https://researchseminars.org/talk/WOPARA/13/ END:VEVENT END:VCALENDAR