Gentry Series: Colloquium – Björn Sandstede

Björn Sandstede, Brown University
Gentry Colloquium: Spiral waves: From phenomena to math and back
ZSR Library Auditorium

For the comfort of all, please refrain from wearing scented products.

Spiral waves are striking spatio-temporal structures that arise in many biological and chemical systems. My goals for this talk are to showcase the wide range of phenomena that spirals exhibit and to illustrate how intuitive concepts such as group velocities and transport can be connected to mathematically rigorous properties such as Fredholm indices and spectral theory. I will then outline how theory helps us understand experimental observations and end with a discussion of two recent surprising results about spectral and linear stability of spiral waves. The first result indicates that planar spiral waves that exhibit transverse instabilities in the far field are spectrally stable but linearly unstable. The second result shows that spiral spectra are discontinuous in the zero-diffusion limit for reaction-diffusion models.