A Conference on Waves, Spectral Theory, and Applications

该项目将为2015年9月10日至11日在新泽西州普林斯顿举行的“海浪、光谱理论和应用”会议的与会者，特别是初级研究人员提供支持。这次会议将汇集非线性偏微分方程组理论和前沿应用方面的专家，这些专家受到非线性科学中波和谱理论研究的巨大影响。会议将讨论的模型在石墨烯、非线性光学、神经科学、大量子系统和拓扑态形成的研究中有应用。这种状态是能量或信息转移或存储的理想状态。另一组重要的数学问题涉及到超材料的设计问题。超材料是一种包括纳米微结构的复合材料。在某些情况下，这些材料表现出自然产生的材料所不具备的特性。例如，可以制造折射率为负或反射为负的超材料，使人们可以将物体“隐形”，使其看不见。这次会议将集中讨论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势相互作用的非线性束缚态的行为。会议的另一个焦点是标准齐化理论范围之外的与超材料有关的问题，以及关于椭圆族的非椭圆极限的问题。有关这次会议的更多细节，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/