Jan 2016: Spot patterns on the surface of the sphere
I'm happy to announce the publication of my paper in the journal Nonlinearity with Michael J. Ward (University of British Columbia) on localized spot patterns on the surface of the sphere. In this paper, we develop the detailed asymptotics that describe the slow dynamics of spot patterns modelled by a system of reaction-diffusion equations. The interesting twist is that when the patterns occur on a surface of non-zero curvature, the methodology must account for higher-order terms due to the changing geometry. It is a wonderful paper with some beautiful mathematics and beautiful pictures.