Research in Elementary Particle Physics

该奖项资助了芝加哥大学杰弗里·哈维教授的研究活动。随着希格斯玻色子的发现，粒子物理学的标准模型现在已经完成，但仍有许多重要的悬而未决的问题涉及物质和能量的基本结构及其相互作用。这些包括理解需要什么样的数学结构来结合引力和量子力学，以及理解暗物质和暗能量的起源。弦理论为解决这些问题提供了一个可能的框架。这个项目的一部分致力于研究在弦理论中发现的新的数学结构，这些结构与研究整数性质的数学领域密切相关。这些新的数学结构也与诸如被称为拓扑绝缘体的新型材料的结构等主题的研究有关，甚至可能与可能用于构建量子计算机的物理系统的研究有关。除了产生新知识之外，该项目还将产生更广泛的影响。它将涉及博士后、研究生，有时也包括本科生，并将为下一代物理学家开始研究提供关键的培训。这一技术知识库为美国开发的许多技术提供了基础，因此加强这一知识库符合国家利益。PI还将在芝加哥地区的国际学校、研讨会和公共宣传活动中演讲。在技术上，PI将扩展他过去在二维共形场理论中赫克算子的作用的工作，并研究在数学物理和凝聚态物理中各种系统的可能应用，其中共形场理论起着核心作用。他还计划研究模形式与有限群表示理论之间联系的新进展，并探索非紧致共形场理论的物理学及其与模拟模形式和弦理论中黑洞熵的联系。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Jeffrey Harvey at the University of Chicago.With the discovery of the Higgs boson, the Standard Model of particle physics is now complete, but there are still many important outstanding questions involving the fundamental structure of matter and energy and their interactions. These include understanding what sorts of mathematical structures are needed to combine gravity and quantum mechanics, as well as to understand the origin of dark matter and dark energy. String theory provides one possible framework in which to address these questions. Part of this project is devoted to the study of new mathematical structures which have been discovered in string theory and which are closely connected to the area of mathematics that studies the properties of whole numbers. These new mathematical structures are also relevant to the study of topics such as the structure of new types of materials called topological insulators and perhaps even to the study of physical systems which may be used to construct quantum computers. This project will also have broader impacts beyond the generation of new knowledge. It will involve postdocs, graduate students, and at times undergraduate students, and will provide critical training for the next generation of physicists as they start research. This pool of technical knowledge provides the foundation for much of the technology developed by the United States, and enhancing this pool of knowledge is therefore in the national interest. The PI will also lecture at international schools and workshops and in public-outreach events in the Chicago area.More technically, the PI will extend his past work on the role of Hecke operators in two-dimensional conformal field theory and investigate possible applications both to mathematical physics and to various systems in condensed-matter physics where conformal field theory plays a central role. He also plans to work on new developments concerning connections between modular forms and the representation theory of finite groups, and to explore the physics of non-compact conformal field theories and their connections to mock modular forms and to black-hole entropy in string theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.