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 日至 20 日在卡热塞科学研究所举行的“TQFT 和分类”会议。拓扑量子场论 (TQFT) 主题提供了一个关键的试验场，理论物理学的思想为严格的数学框架提供了基础，为量子引力理论奠定了基础。 TQFT 在 3 维方面得到了特别深入的研究，带来了数学和理论物理之间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），因此真正理解它需要将 3 维 TQFT 技术扩展到 4 维。 这种数学结构的增强被称为“分类”。 本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”会议旨在围绕将技术从3维TQFT研究提升到4维的中心问题，聚集来自不同领域的研究人员。 会议将围绕三个中心主题组织：Heegaard-Floer 同调和辛几何、代数分类（包括霍瓦诺夫同调、分类量子群和统一根分类）和 TQFT（包括与物理、超同调和非半简单不变量的联系）。组织者希望这次会议能够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，请访问 https://tqft.sciencesconf.org/ 该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。