分析和微分方程讨论班——Quantum Invariants for 3-Manifolds with Boundary

Abstract:

In this talk, we introduce the 3-alterfold with a separating surface. When the separating surface is decorated by a spherical fusion category, we obtain quantum invariants of 3-alterfold, which is consistent with many topological moves. These moves provide evaluation algorithms for various presentations of $3$-alterfold, e.g. Heegaard splittings, triangulations, link surgeries. In particular, we obtain quantum invariants of 3-manifolds containing surfaces, generalizing those of 3-manifolds containing framed links. Moreover, in this framework, we topologize fundamental algebraic concepts. For instance, we implement the Drinfeld center by tube diagrams as a blow up of framed links. The topologized center leads to a quick proof of the equality between the Reshetikhin-Turaev invariants and the Turaev-Viro invariants for spherical fusion categories. In addition, we topologize half-braiding, $S$-matrix and the generalized Frobenius-Schur indicators, etc.

报告人简介： 

北大本科，中科院博士。曾就职于中国科学技术大学，哈尔滨工业大学，现在为北京雁栖湖应用数学研究院教授。 主要研究方向为泛函分析、算子代数及其在量子信息中的应用。吴教授及其合作者开拓了量子傅里叶分析，为量子信息的研究提供了数学工具。学术论文发表在PNAS, Adv. Math., Comm. Math. Phys., J. Funct. Anal. , Israel J. Math.等著名期刊。