Topological Quantum Field Theory and Categorification

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日在法国Cargese科学研究所举行的“TQFT和分类”会议。拓扑量子场论（TQFT）的主题提供了一个重要的试验场，理论物理学的思想为奠定量子引力理论基础的严格数学框架提供了信息。在三维空间中，tqft得到了很好的研究，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四维的（包括时间），真正理解它需要将三维tqft的技术扩展到四维。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，以了解四维tqft，同时为建立新的合作关系和青年科学家的科学发展提供重要机会。“TQFT与分类”会议旨在将来自不同领域的研究人员聚集在一起，围绕将技术从三维TQFT研究提升到四维的中心问题。会议将围绕三个中心主题组织：Heegaard-Floer同调和对称几何，代数分类（包括Khovanov同调，有分类的量子群和单位根的分类）和TQFT（包括与物理学的联系，超同调和非半单不变量）。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。关于本次会议的更多信息可以在https://tqft.sciencesconf.org/This上找到，奖项反映了NSF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 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.