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Texas A&M University
Mathematics

Hiring Candidate - Dr. Shawn Cui

Date: January 22, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Dr. Shawn Cui , Stanford University

  

Description:

Title: Four Dimensional Topological Quantum Field Theories

Abstract:

We give an introduction to topological quantum field theories (TQFTs) which have wide applications in low dimensional topology, representation theory, and topological quantum computing. In particular, TQFTs provide invariants of smooth manifolds. We give an explicit construction of a family of four dimensional TQFTs. The input to the construction is a class of tensor categories called $G$-crossed braided fusion categories where $G$ is any finite group. We show that our TQFTs generalize most known ones such as Yetter's TQFT and Crane-Yetter TQFT. It remains to check if the resulting invariant of 4-manifolds is sensitive to smooth structures. It is expected that the most general four dimensional TQFTs should be from a spherical fusion 2-category whose definition has not been universally agreed.
We prove that a $G$-crossed braided fusion category corresponds to a 2-category which does not satisfy the criteria of a spherical fusion 2-category defined by Mackaay. Thus the question of what axioms properly define a spherical fusion 2-category is open.
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