The APDE seminar on Monday, 10/30, will be given by Yuzhou (Joey) Zou (Northwestern) in-person in **Evans 736,** and will also be broadcasted online via Zoom from **4:10pm to 5:00pm PST**. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

**Title:** Weighted X-ray mapping properties on the Euclidean and Hyperbolic Disks

**Abstract:** We discuss recent works studying the sharp mapping properties of weighted X-ray transforms and weighted normal operators. These include a C^\infty isomorphism result for certain weighted normal operators on the Euclidean disk, whose proof involves studying the spectrum of a distinguished Keldysh-type degenerate elliptic differential operator. We also discuss further work studying additional self-adjoint realizations of this operator, using the machinery of boundary triplets. In addition, we discuss ongoing work which applies these results to the X-ray transform on the hyperbolic disk by using a projective equivalence between the Euclidean and hyperbolic disks. Joint works with N. Eptaminitakis, R. K. Mishra, and F. Monard.