Björn Sandstede
Björn Sandstede
Most of my past and current research projects are concerned with understanding the formation of patterns and the dynamics of nonlinear waves in spatially extended systems. Extended systems are typically modelled by partial differential equations on unbounded domains. Nonlinear waves correspond to interfaces, or defects, that are formed between co-existing patterns. These patterns, as well as the defects and interfaces formed between them, are found in many biological, chemical, and physical applications. Examples are the transmission of signals in optical fibers, the formation of hexagonal and stripe patterns in fluid convection, and the generation of spiral waves in catalytic chemical reactions. Motivated by experiments and numerical simulations, I aim to understand when and how patterns and defects are formed, how they behave under small perturbations, what other patterns or waves with a more complicated spatio-temporal behaviour can bifurcate from them, and how they interact with each other or with domain boundaries. To answer these questions, I use a mixture of analytical and geometric dynamical-systems techniques, and I have also developed numerical algorithms for the computation of waves and their bifurcations.
More details of some of my recent and current projects can be found on this overview page.
Information about recent reading groups and graduate schools can be found on my teaching page.
Links to audio/video/PDF recordings of talks I have given: