Joel Andersson: Selected topics on the weighted Radon transform

** Note the change of time! **

In this talk I will discuss invertibility of the weighted Radon (or X-ray) transform in dimension 2.

The first part of the talk will be more of a survey. I will define the various transforms, selected breakthroughs in terms of inversion formulae and perhaps mention some interesting problems and applications.

In the second part I will focus on the so-called local injectivity problem and present some of my most recent results. If time allows I hope to at least communicate the basic ideas on how one can get stability estimates for the local weighted Radon transform. For this purpose it will be enough for us to focus on constant weights, i.e. consider the standard Radon transform in the plane.