Key collaborator: Anthony Yeates
A long-running thread in my research concerns the mathematical foundations of linking, magnetic helicity, and geometric measures of entanglement such as writhe (and its relationship to twist/self-linking). Rather than addressing a single isolated “problem”, the aim is to develop a precise and usable understanding of concepts that are widely invoked across many fields (e.g. magnetic field evolution in plasmas, DNA topology), but are often defined ambiguously or used without a clear separation between topology, geometry and gauge.
Entanglement of curves and field lines is not merely a visual feature: it can constrain dynamics, store energy, and impose conservation laws. Quantities such as linking number, helicity, writhe and twist appear across magnetohydrodynamics, fluid mechanics, elasticity of rods and filaments, and biopolymers. A recurring theme of this work is to connect classical topological invariants with definitions that remain meaningful in physically realistic geometries, including open domains and boundary-dominated settings.