EVENT DETAILS AND ABSTRACT

Title: Microlocal analysis of the geodesic X-ray transform with conjugate points of fold type
Speaker: Plamen Stefanov
Speaker Info: Purdue University
Brief Description:
Special Note:
Abstract:

We study the geodesic X-ray transform with conjugate points of fold type. Assuming that we know this transform of some function near one such geodesic, the question which we are trying to answer is: can we recover the wave front set of the function conormal to that geodesic? We describe the microlocal structure of the transform which leads to an FIO with a Lagrangian given by the conormal bundle of the conjugate locus. We show that in some cases we can invert it microlocally but in some other cases we cannot. This is a joint work with Gunther Uhlmann.