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日在卡热塞科学研究所举行的“TQFT和分类”会议。 拓扑量子场论（TQFT）的主题提供了一个关键的试验场，来自理论物理学的想法为严格的数学框架提供了信息，为量子引力理论奠定了基础。 TQFT在3维空间中得到了很好的研究，在数学和理论物理之间带来了前所未有的互动。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技术扩展到四维。 这种数学结构的增强被称为“范畴化”。 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和年轻科学家的科学发展提供重要的机会。“TQFT和分类”会议旨在汇集来自不同领域的研究人员，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同调和辛几何，代数学分类（包括Khovanov同调，分类量子群和统一根的分类）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能够成为建立持久合作和新的研究途径的催化剂。关于这次会议的更多信息可以在www.example.com上找到https://tqft.sciencesconf.org/This奖项反映了NSF的法定使命，并被认为值得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来支持。

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.