Noncommutative Geometry Seminar

Date: March 29, 2024

Time: 10:00AM - 11:00PM

Location: BLOC 306

Speaker: Zhengwei Liu , Tsinghua University

Title: Alterfold Topological Quantum Field Theory

Abstract: We will introduce the 3-alterfold Topological Quantum Field Theory (TQFT). It is a 3D TQFT with space-time boundary, which encodes Jones' theory of planar algebras as a local theory on the 2D boundary. Both Turaev-Viro (TV) TQFT and the Reshetikhin-Turaev (RT) TQFT can be naturally embedded in the alterflold TQFT through blow-up procedures. We provide 3D topologization of various key concepts, such as the Drinfeld center, connections, Frobenius-Schur indicators, etc. Many remarkable results become apparent in this approach, including the equivalence between TV TQFT and RT TQFT. This is recent work joint with Shuang Ming, Yilong Wang and Jinsong Wu, see arXiv:2307.12284 and arXiv:2312.06477. For lectures in the next week, we will introduce the alterfold theory in all dimensions and construct infinite TQFT. We will discuss its connections with operator algebras, topological orders, higher categories, etc. We propose an approach to Poincare conjecture through renormalizations.