Adam Larios

Are there equations in mathematics that are justtoo hard to solve? Perhaps–and many of them seem to be nonlin-ear partial differential equations. But we cannot give up! Theseequations appear in nearly every scientific discipline, includingphysics, biology, chemistry, medicine, so we must work towardsan understanding of these equations if we are going to makeprogress in science. Fortunately, there is a certain tool that canunwrap a large amount of the complexity of these equations,which is both elegant and powerful–namely, Fourier spectralanalysis. We will see how this tool can be used to understandthe behavior of equations governing heat flow, traffic flow, wa-ter waves, and flame fronts. This talk should be accessible tostudents who have taken calculus.