ACDC Seminar/Colloquium by Dan Hill on the 25th of March

On 25-03-2026 at 16:00, Dan Hill (Oxford) will give an Amsterdam Dynamics Seminar/Colloquium talk. Note that this is both a general colloquium as a dynamics seminar. We will go for drinks at Bar Boele after the talk.

The talk will take place in the Maryam seminar room (9A-46).

Title:  Think Global, Act Local: Inducing Fully Localised 2D Patterns via Spatial Heterogeneity

Abstract: The existence of localised two-dimensional patterns has been observed and studied in numerous experiments and simulations: ranging from optical solitons, to patches of desert vegetation, to fluid convection. And yet, our mathematical understanding of these emerging structures remains extremely limited beyond one-dimensional examples.

In this talk I will discuss how adding a compact region of spatial heterogeneity to a PDE model can not only induce the emergence of fully localised 2D patterns, but also allows us to rigorously prove and characterise their bifurcation. The idea is inspired by experimental and numerical studies of magnetic fluids and tornados, where our compact heterogeneity corresponds to a local spike in the magnetic field and temperature gradient, respectively. In particular, we obtain local bifurcation results for fully localised patterns both with and without radial or dihedral symmetry, and rigorously continue these solutions to large amplitude. Notably, the initial bifurcating solution (which can be stable at bifurcation) varies between a radially-symmetric spot and a 'dipole' solution as the width of the spatial heterogeneity increases.This work is in collaboration with David J.B. Lloyd and Matthew R. Turner (both University of Surrey).

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