Abstract: In this talk I will discuss recent progress in the analysis
of geodesic ray transforms and their relevance for the solution of
some geometric inverse problems
on Riemannian manifolds. The standard X-ray transform, where one
integrates a function along straight lines is a well-studied object
(and the basis of several medical imaging techniques), but I will
consider more general transforms in which we integrate tensor fields
along geodesics of a certain Riemannian metric.
These transforms arise naturally as linearizations of important
geometric inverse problems like the boundary rigidity problem in which
one tries to determine a Riemannian metric from the knowledge of its
boundary distance function. The talk is based on joint work with Mikko Salo
and Gunther Uhlmann.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006