From Topological Defects to Morphogenesis: Liquid Crystals on Curved and Evolving Surfaces

Farzan Vafa, Assistant Professor, Niels Bohr Institute, University of Copenhagen

In this talk, we explore the interplay between liquid crystals and surfaces, focusing on the role of topological defects. Starting with liquid crystals on cones, we demonstrate how defects are absorbed and emitted at the cone apex. Extending this framework to active nematics, we uncover rich defect dynamics such as periodic orbits, pair nucleation, and unbinding at the apex. We then apply this framework to epithelial morphogenesis, where allowing the surface to evolve via relaxational dynamics leads to a geometric diffusion equation in which topological defects nucleate curvature. We relate this result to generic observations of topological defects nucleating curvature in epithelial tissues, for example tentacle formation in the marine invertebrate Hydra. Our analytical results are corroborated by numerical simulations.