Department of Mathematics Colloquium

Date/Time/Room: Thursday (4/5/2001) at 3:00pm in 304 PKH

Speaker: Timothy Callahan, Department of Mathematics, University of Michigan

``Pattern Formation and Equivariant Bifurcation Theory''

Abstract: Many systems exhibit the striking phenomenon of pattern formation, the process by which an initially spatially uniform state loses stability to a state with a characteristic length scale: a pattern. The variety of systems that undergo such a process is if anything even more striking, and ranges from fluid dynamics to geology to neurology to nonlinear optics to video feedback to embryonic development. The ubiquity of such patterns can be explained by equivariant bifurcation theory, which uses group-theoretic methods and the symmetry of the problem to make predictions that are independent of the model. I will present an introduction to the theory and the mathematical tools it employs.