Topological Quantum Field Theory and Categorification

拓扑量子场论及其分类

• 批准号: 1806399
• 负责人: Aaron Lauda
• 金额: $ 1.8万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-03-15 至 2019-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1806399&HistoricalAwards=false
• 关键词: Topological; Quantum; Field; Theory; Categorification

This award will fund the participation of US-based junior researchers in the "TQFT and Categorification" conference to be held at the Institut d'Etudes Scientifiques de Cargese on April 15-20, 2018. The subject of Topological Quantum Field Theory (TQFT) has provided a critical testing ground where ideas from theoretical physics inform rigorous mathematical frameworks that lay the foundation for a quantum theory of gravity. TQFTs have been particularly well studied in 3-dimensions, bringing about unprecedented interaction between mathematics and theoretical physics. Since the world we live in is 4-dimensional (including time), truly understand it requires an extension of the techniques of 3-dimensional TQFTs into 4-dimensions. This enhancement of mathematical structures has come to be called "Categorification". This conference will advance this ambitious program to understand 4-dimensional TQFTs, while proving important opportunities for the establishment of new collaborations and the scientific development of young scientists.The "TQFT and Categorification" conference aims to bring together researchers from different horizons around the central question of lifting the techniques from the study of 3-dimensional TQFTs to 4-dimensions. The conference will be organized around three central themes: Heegaard-Floer homologies and symplectic geometry, Algebraic categorification (including Khovanov homology, categorified quantum groups, and categorification at roots of the unity), and TQFT (including connections to physics, super homologies, and non-semisimple invariants). The organizers expect this conference to be a catalyst for establishing lasting collaborations and new avenues of research. More information about this conference can be found at https://tqft.sciencesconf.org/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.

该奖项将资助基于美国的初级研究人员参加“ TQFT和分类”会议，该会议将于2018年4月15日至20日在Cargese Institut d'Etudes eTudifiques de Cargese举行。拓扑量子场理论（TQFT）的主题提供了一个关键的测试基础，从而使严格的物理学层面的思想构成了基础的基础。 TQFT在三维中进行了尤其充分的研究，从而在数学与理论物理学之间产生了前所未有的相互作用。由于我们生活的世界是4维（包括时间），因此真正了解它需要将3维TQFT的技术扩展为4维。 数学结构的这种增强已被称为“分类”。 这次会议将推进这项雄心勃勃的计划，以了解4维TQFTS，同时证明了建立新的合作和年轻科学家的科学发展的重要机会。“ TQFT和分类”会议旨在将来自不同视野的研究人员聚集在不同地平线的研究人员中，从而将3维TQFTS研究从3二维TQFTS研究中提升到4二维的研究中。 会议将在三个中心主题周围组织：Heegaard-loer同源性和符号几何形状，代数分类（包括Khovanov同源性，分类量子组和Unity根源的分类），以及TQFT（包括与物理学，超级同源性的连接，超级同源性和非犹太人的连接）。组织者希望这次会议成为建立持久合作和新研究途径的催化剂。有关本次会议的更多信息，请参见https://tqft.sciencesconf.org/this Award反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，认为值得通过评估来获得支持。