The geodesic X-ray transform: a semiclassical approach and applications to asymptotically conic spaces (Joint with IP seminar)

The geodesic X-ray transform of a function on a manifold is
the map associating to each geodesic the integral of the function
along the geodesic, defined under appropriate conditions. A basic
question is the injectivity of this transform, together with estimates
for the left inverse, and possible algorithms for constructing such a
left inverse. Much progress has been made on this, as well as
non-linear extensions, such as the boundary rigidity problem, over the
past decade. I will discuss more recent work on this both in the
context of bounded domains and in asymptotically conic spaces, the
latter being joint work with Evangelie Zachos.