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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
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Events
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Forum
Life @ BIMSA
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Transportation
Facilities
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News
News
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Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Moscow-Beijing topology seminar Tensor categories and alterfold theory
Tensor categories and alterfold theory
Organizers
Vassily Manturov , Shiquan Ren , Zhe Yan Wan
Speaker
Shuang Ming
Time
Wednesday, August 7, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 831 5020 0580 (141592)
Abstract
In this talk, I will introduce a partition function defined on bi-colored three-manifolds decorated by tensor diagrams from a spherical fusion category \mathcal{C}. We called them 3 dimensional alterfold. This partition function yields three-manifold invariants and three-dimensional topological quantum field theories (TQFTs). I will discuss how well-known invariants and TQFTs, such as Turaev-Viro theory and Reshetikhin-Turaev theory, can be naturally embedded within our framework. Furthermore, our bi-colored theory provides topological interpretations for fundamental concepts in tensor categories, including the Drinfeld center and Frobenius-Schur indicators. We expect the theory could generalizes to higher dimensions, and could produce new identities for (higher) tensor categories.
Beijing Institute of Mathematical Sciences and Applications
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