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.

该奖项将资助美国的初级研究人员参加将于2018年4月15-20日在Cargese学院举行的“TQFT与分类”会议。拓扑量子场论(TQFT)的主题提供了一个关键的试验场，在这里，来自理论物理的想法形成了严格的数学框架，为量子引力理论奠定了基础。全量子傅立叶变换在三维空间中的研究尤为深入，在数学和理论物理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维的(包括时间)，真正理解它需要将3维TQFT的技术扩展到4维。这种对数学结构的改进被称为“范式化”。这次会议将推进这一雄心勃勃的计划，以了解4维TQFT，同时为建立新的合作关系和年轻科学家的科学发展提供重要机会。“TQFT和分类”会议旨在将来自不同视野的研究人员聚集在一起，围绕将技术从三维TQFT研究提升到4维这一中心问题。会议将围绕三个中心主题组织：Heegaard-Floer同调和辛几何、代数范畴化(包括Khovanov同调、范畴化量子群和单位根处的范畴化)和TQFT(包括与物理、超同调和非半单不变量的联系)。组织者希望这次会议成为建立持久合作和新的研究途径的催化剂。有关这次会议的更多信息可以在https://tqft.sciencesconf.org/This网站上找到，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智力优势和更广泛的影响审查标准进行评估，被认为值得支持。