Pure mathematics

  • Article
    | Open Access

    Classifying groups is an important challenge in mathematics and has led to the identification of groups which do not belong to the main families. Here Duncan et al. introduce a type of moonshine which is a connection between these groups, number theory and potentially physics.

    • John F. R. Duncan
    • , Michael H. Mertens
    •  & Ken Ono
  • Article
    | Open Access

    Strings or long chains are prone to knotting. Here, the authors demonstrate that the vortex structure of quantum wavefunctions, such as that in a simple harmonic oscillator, can also contain knots, whose topological complexity can be a descriptor of the spatial order of the system.

    • Alexander J. Taylor
    •  & Mark R. Dennis