Dave Lloyd is visiting the Department of Mathematics at Imperial College London today (Thursday 25 January), to give a talk in the Dynamical Systems Seminar Series. The title of his talk is “Advances in the analysis of multidimensional localised patterns“. His talk will present recent results on developing centre-manifold reduction methods for multidimensional localised patterns. In the first part of the talk, he will concentrate on axisymmetric spikes emerging from the surface of a magnetic fluid. It is shown how the ferrofluid problem (modelled by the Navier-Stokes equation coupled to Maxwell’s equations) can be decomposed into an infinite-system of coupled radial ODEs where invariant manifold theory can be applied to show the existence of various types of axisymmetric patterns. In the second half of the talk, he will present an approximate theory for more complicated localised patches involving general dihedral cellular patterns where again radial invariant manifold theory can be used. The image below is from his latest paper “Dihedral rings of patterns emerging from a Turing bifurcation” soon to appear in Nonlinearity.