A Conference on Waves, Spectral Theory, and Applications

University Of North Carolina At Chapel Hill, Chapel Hill NC

Investigators

Abstract

This project will provide support for participants, especially junior researchers, in the conference "Waves, Spectral Theory, and Applications" in Princeton, NJ from September 10-11, 2015. This conference will bring together experts in both the theory of nonlinear partial differential equations and cutting edge applications, which are dramatically impacted by the study of waves and spectral theory in nonlinear science. The models to be discussed at the conference have applications to the studies of graphene, nonlinear optics, neuroscience, large quantum systems, and the formation of topological states. Such states are ideal for the transfer or storage of energy or information. Another important set of mathematical problems concerns the issues for design of metamaterials. Metamaterials are composites that include nano-size microstructures. In some regimes these materials exhibit properties not achievable in naturally occurring materials. For example, it is possible to manufacture a metamaterial with negative index or reflection that allows one to "cloak" objects, making them invisible. The conference will focus on the issues of spectral theory and nonlinear dynamics that are instrumental for understanding the behavior of nonlinear bound states interacting with various types of potentials. Another focus of the conference is on the metameterials-related problems that lie outside the realm of standard homogenization theory as well as to problems concerning non-elliptic limits of families of elliptic problems. More details about the conference can be found at https://sites.google.com/site/wavesandspectraltheory/