Tu, October 29, 2024, 9:00-10:00 am PDT via Zoom:
Yuzhou (Joey) Zou (Northwestern University, USA).
Title: The X-Ray Transform on Euclidean and Hyperbolic Disks via Projective Equivalence
Abstract: We discuss recent works studying sharp mapping properties of weighted X-ray transforms on the Euclidean disk and hyperbolic disk. We are particularly interested in the mapping properties of weighted versions of normal operators associated to the X-ray transform and the behavior of such operators up to the boundary; the presence of weights sometimes improves such behavior. We prove a C^\infty isomorphism result (joint with R. Mishra and F. Monard) for certain weighted normal operators on the Euclidean disk by studying the spectrum of a distinguished Keldysh-type degenerate elliptic differential operator. We then discuss how to transfer these results to the hyperbolic disk (joint with N. Eptaminitakis and F. Monard), by using a projective equivalence between the Euclidean and hyperbolic disks via the Beltrami-Klein model, where one can view geodesics in the hyperbolic disk as Euclidean geodesics up to reparametrization.
Tu, November 12, 2024, 9:00-10:00 am PST via Zoom:
Lili Yan (University of Minnesota, USA).
Title: TBA
Abstract: TBA
Tu, November 26, 2024, 9:00-10:00 am PDT via Zoom:
Giovanni Covi (
University of Helsinki, Finland).
Title: TBA
Abstract: TBA