Artifacts in the inversion of some ray transforms with conjugate points in two dimensions (Joint w/ IP seminar) 

 Abstract:  In this talk, we first consider the integral transform over
a general family of broken rays in $\mathbb{R}^2$. One example of the
broken rays is the family of rays reflected from a curved boundary
once. There is a natural notion of conjugate points for broken rays.
If there are conjugate points, we show that the singularities conormal
to the broken rays cannot be recovered from local data and therefore
artifacts arise in the reconstruction. As for global data, more
singularities might be recoverable. Then we show that such results can
be generalized to the case of the integral transform over a generic
family of smooth curves.