Seminarium Teorii Względności i Grawitacji

This talk is an overview of the research topics that form the basis of the POLS fellowship I have recently been awarded by the National Science Centre. I will start with an introduction of the fellowship including its nature, its aims and structure, together with a summary of my research career to date. I will then review the mathematical developments arising from the study of non-shearing congruences of null geodesics, which played a central role during the Golden Age of Relativity, and which would later shape many geometrical ideas, notably in connection with spinors, conformal and complex geometries. I will also cover a survey of more recent results in the field including generalisations to higher dimensions, thereby providing a motivation for the objectives of the POLS fellowship.