Professor Sandstede’s research focuses on understanding the formation and the dynamics of patterns and nonlinear waves in spatially extended systems. He has worked on the foundations of pattern formation through the development of analytical, geometric, numerical, and statistical techniques. Applications considered include data assimilation, traffic flow, infectious disease propagation on networks, nonlinear optical fibers, and biological applications such as spatial differentiation in zebrafish and mRNA localization in Xenopus oocytes. More recently, he has also started to work on data analysis, focusing on preconditioning of data for a subsequent topological data analysis.
Professor, Division of Applied Mathematics