David Lloyd (Surrey) – Snakes on the plane: Developing a theory of Multidimensional Localised Patterns

In this talk, I will review some of the recent advances in developing mathematical and computational methods for 1D localised patterns (patterns that are embedded in a quiescent state) to 2D localised patterns. These patterns occur in a wide range of applications from buckling of cylinders, vegetation patches near deserts, to fluid mechanics. While the mathematical theory of these patterns in 1D is well-established in higher-dimensions, new tools are required. This work has appeared on the front cover of JFM 2015 and the January 2024 Nonlinearity journal, nominated for the IMA Lighthill-Thwaites prize 2021, and subject of the SIAM 2024 T. Brooke Benjamin prize.