Viruses Under a Mathematical Microscope: From Viral Geometry to Virus Nanotechnology

The geometric principles underpinning virus structure provide a key to understanding viral infections akin to a "Mathematical Microscope". Most viruses have a protein shell, called viral capsid, that surrounds, and thus protects, the genetic material. Mathematical techniques from group, graph and tiling theory enable classification of capsid architecture in terms of surface lattices that encode the positions of individual capsid proteins and the interactions between them. By combining these geometric, and related topological, descriptors of virus architecture with stochastic simulations, I will demonstrate how viral geometry provides insights into viral life cycles that pave the way to innovation in antiviral therapy and virus nanotechnology.