Title: Geometric methods in inverse problems
Organizer(s): Matti Lassas, University of Helsinki
Speakers: Lauri Oksanen, University of Helsinki
Inverse problem for the wave equation with one measurement and the scattering relation

Leo Tzou, University of Arizona
The Aharonov-Bohm effect and the Calderón problem for connection Laplacians

Pilar Herreros, University of Munster
Lens rigidity for surfaces with trapped geodesics

Plamen Stefanov, Purdue University
The identification problem in SPECT: uniqueness, non-uniqueness and stability
Andras Vasy, Stanford University (cancelled)
Hiroshi Isozaki, University of Tsukuba (cancelled)
Katya Krupchyk, University of Helsinki (cancelled)
Mikko Salo, University of Helsinki (cancelled)
Abstract: The workshop will cover a wide range of new developments in geometric inverse problems on elliptic and hyperbolic equations and spectral problems. Also, the workshop deals on the use of geometric methods to solve analytic inverse problems for various partial differential equations in Euclidean domains. As an example of geometric inverse problems one may consider the determination of the variable wave propagation speed in a domain from the boundary measurements. The travel time of the waves between two points defines a natural distance between the points. This is called the travel time metric. A classical inverse problem is to determine the wave speed inside the object when we know the travel times between the boundary points. This problem is an idealization of the geophysical problem where the structure of the Earth is to be found from the travel times of earthquakes through the Earth. In many imaging methods, including the medical ultrasound imaging and geophysical prospecting, reconstructions are done in the travel time coordinates. In all these problems the determination of the wave speed corresponds to the reconstruction of a Riemannian metric associated to the wave velocity.

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