Mathematical Physics and Harmonic Analysis Seminar

Date: January 27, 2023

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Gaik Ambartsoumian, University of Texas at Arlington

Title: On integral geometry using objects with corners

Abstract: Integral geometry is dedicated to the study of integral transforms mapping a function (or more generally, a tensor field) defined on a manifold to a family of its integrals over certain submanifolds. A classical example of such an operator is the Radon transform, mapping a function to its integrals over hyperplanes. Generalizations of that transform integrating along smooth curves and surfaces (circles, ellipses, spheres, etc) have been studied at great length for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. This talks will discuss some recent results about Radon-type transforms that have a “corner” in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).