Spinors, which can be thought of as "square roots" of vectors, play a key role in differential geometry (the study of multidimensional smooth, curved spaces), with beautiful and often surprising connections to many areas within the subject. The most famous examples are the so-called Killing spinors, which are by now well understood to occur only in certain very special situations, and whose existence imposes strong constraints on the shape of the underlying space. Killing spinors and their lesser known cousins are also important objects in mathematical physics, where they are related to string theory and supersymmetry, and in the study of immersion theory (how we can "embed" spaces inside larger spaces) and G-structures (what sort of symmetries different spaces have) in low dimensions. In this introductory talk I will give a bird's eye view of some of these connections, and briefly explain my current research project of finding spinors on certain highly symmetric spaces.
Jordan Hofmann works in differential geometry, and obtained her PhD from King's College London in 2023. She has previously been a postdoctoral researcher at King's College London and Philipps-Universität Marburg, and was a Lecturer (Teaching) at University College London. From June to September 2025, she is a Junior Fellow at the Alfried Krupp Wissenschaftskolleg Greifswald.
Moderation: Professorin Dr. Ines Kath