Date

Re­search sem­in­ar "Geo­met­ric and Har­mon­ic Ana­lys­is": Nikolas Eptamin­i­ta­kis (Han­nov­er), The Geodes­ic X-Ray Trans­form on the Hy­per­bol­ic Disk

Location: D2.314

Abstract: Given a Riemannian manifold, the geodesic X-ray transform of a 
function or tensor field is defined by its line integrals over 
geodesics, and it is a central object in geometric inverse problems. In 
this talk, we will focus on the X-ray transform in the classical 
geometric setting of two-dimensional hyperbolic space. This setting is 
particularly interesting due to its lack of compactness and its role as 
a model for more general geometries, such as asymptotically hyperbolic 
spaces. We will report on recent progress in characterizing the range of 
the geodesic X-ray transform in this setting, deriving singular value 
decompositions, establishing sharp mapping properties, and developing 
reconstruction procedures. Based on joint work with François Monard and 
Yuzhou Zou.

If you are interested in participating online please contact  Tobias Weich or Benjamin Delarue in order to receive the login details.