School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

University of Cambridge

In this talk I will discuss recent progress in the analysis

Abstract:

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