A Conference on Waves, Spectral Theory, and Applications

该项目将为参与者提供支持，特别是初级研究人员，在会议“波，谱理论和应用”在普林斯顿，新泽西州从2015年9月10日至11日。本次会议将汇集非线性偏微分方程理论和前沿应用的专家，这些应用受到非线性科学中波和谱理论研究的巨大影响。会议上讨论的模型可应用于石墨烯，非线性光学，神经科学，大型量子系统和拓扑状态的形成的研究。 这种状态对于能量或信息的传输或存储是理想的。另一组重要的数学问题涉及超材料的设计问题。超材料是包括纳米尺寸微结构的复合材料。在某些情况下，这些材料表现出在天然存在的材料中无法实现的性质。例如，有可能制造一种具有负折射率或反射的超材料，允许人们“隐藏”物体，使其不可见。 会议将集中讨论光谱理论和非线性动力学问题，这些问题有助于理解与各种类型的势相互作用的非线性束缚态的行为。会议的另一个重点是关于标准均匀化理论领域之外的与超材料相关的问题，以及关于椭圆问题族的非椭圆极限的问题。有关会议的更多详细信息，请访问https://sites.google.com/site/wavesandspectraltheory/

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/