Triangle Seminars
Tuesday, 7 Apr 2026
Insights from the crosscap state toward non-orientable TQFTs
📍 London
Ippo Orii
(IPMU, U Tokyo)
Abstract:
Quantum London Seminar (QMUL+LIMS joint seminar).
Talk info can be found on https://lims.ac.uk/
A topological quantum field theory (TQFT) is a class of field theories that have been successfully formulated in a mathematically rigorous way, providing a framework for describing physical phenomena independent of the spacetime metric. In particular, (2+1)-dimensional TQFTs—exemplified by Chern–Simons theory—have been extensively studied in both high-energy and condensed-matter physics as toy models of low-dimensional quantum gravity and as effective theories describing the fractional quantum Hall effect.
TQFTs with time-reversal symmetry are equivalent to considering such theories on non-orientable manifolds. However, While these systems exhibit rich mathematical structures, many physical aspects remain unresolved, and a complete mathematical formulation is still lacking. Among the most important objects for analyzing time-reversal-symmetric TQFTs is the crosscap state, which captures the essential features of non-orientable TQFTs.
In this talk, I will provide an overview of the current understanding of systems with time-reversal symmetry through the study of crosscap states, incorporating some of my recent results. And I will also present a new idea suggesting that the study of crosscap states may contain key insights toward a rigorous formulation of non-orientable TQFTs.
Quantum London Seminar (QMUL+LIMS joint seminar).
Talk info can be found on https://lims.ac.uk/
A topological quantum field theory (TQFT) is a class of field theories that have been successfully formulated in a mathematically rigorous way, providing a framework for describing physical phenomena independent of the spacetime metric. In particular, (2+1)-dimensional TQFTs—exemplified by Chern–Simons theory—have been extensively studied in both high-energy and condensed-matter physics as toy models of low-dimensional quantum gravity and as effective theories describing the fractional quantum Hall effect.
TQFTs with time-reversal symmetry are equivalent to considering such theories on non-orientable manifolds. However, While these systems exhibit rich mathematical structures, many physical aspects remain unresolved, and a complete mathematical formulation is still lacking. Among the most important objects for analyzing time-reversal-symmetric TQFTs is the crosscap state, which captures the essential features of non-orientable TQFTs.
In this talk, I will provide an overview of the current understanding of systems with time-reversal symmetry through the study of crosscap states, incorporating some of my recent results. And I will also present a new idea suggesting that the study of crosscap states may contain key insights toward a rigorous formulation of non-orientable TQFTs.
Posted by: JUVEN WANG
Geometric Categories for Continuous Gauging
📍 London
Matthew Yu
(Oxford)
Abstract:
Quantum London Seminar (QMUL+LIMS joint seminar).
Talk info can be found on https://lims.ac.uk/
I will present a unified categorical framework which encodes gauging of continuous and finite symmetries in arbitrary spacetime dimension. I will show how this framework can identify electric and magnetic symmetries expected in G-gauge theory, and how to capture electric symmetry breaking resulting from the addition of charged matter. I introduce geometric categories, i.e. categories internal to stacks. This allows us to extend (de)equivariantization of fusion categories to continuous groups, construct a functorial SymTFT and boundaries for this theory, and compute the relevant categories of endomorphisms and Drinfeld centers.
Quantum London Seminar (QMUL+LIMS joint seminar).
Talk info can be found on https://lims.ac.uk/
I will present a unified categorical framework which encodes gauging of continuous and finite symmetries in arbitrary spacetime dimension. I will show how this framework can identify electric and magnetic symmetries expected in G-gauge theory, and how to capture electric symmetry breaking resulting from the addition of charged matter. I introduce geometric categories, i.e. categories internal to stacks. This allows us to extend (de)equivariantization of fusion categories to continuous groups, construct a functorial SymTFT and boundaries for this theory, and compute the relevant categories of endomorphisms and Drinfeld centers.
Posted by: JUVEN WANG
Thursday, 9 Apr 2026
Anomalies in Topological Orders: From Algebraic Topology to Physical Realizations
📍 London
Weicheng Ye
(UBC)
Abstract:
Quantum London Seminar (QMUL+LIMS joint seminar).
Talk info can be found on https://lims.ac.uk/
Topological orders are fascinating objects with profound
applications across mathematical physics, condensed matter physics,
and quantum information science. This talk explores the critical
interplay between anomalous symmetry actions of topological orders and
their physical realizations. I will begin by formalizing the
mathematical definition of anomalies in topological orders, framing
them as rigorous lifting obstructions in algebraic topology. Building
on this foundation, I will introduce diagrammatic techniques for
calculating these anomalies explicitly. Finally, I will demonstrate
how these mathematical anomalies dictate whether a given topological
order can be physically realized in lattice systems or quantum field
theories through the framework of anomaly matching.
This talk is based on arXiv: 2210.02444, 2309.15118, 2312.13341, and 2510.24834.
Quantum London Seminar (QMUL+LIMS joint seminar).
Talk info can be found on https://lims.ac.uk/
Topological orders are fascinating objects with profound
applications across mathematical physics, condensed matter physics,
and quantum information science. This talk explores the critical
interplay between anomalous symmetry actions of topological orders and
their physical realizations. I will begin by formalizing the
mathematical definition of anomalies in topological orders, framing
them as rigorous lifting obstructions in algebraic topology. Building
on this foundation, I will introduce diagrammatic techniques for
calculating these anomalies explicitly. Finally, I will demonstrate
how these mathematical anomalies dictate whether a given topological
order can be physically realized in lattice systems or quantum field
theories through the framework of anomaly matching.
This talk is based on arXiv: 2210.02444, 2309.15118, 2312.13341, and 2510.24834.
Posted by: JUVEN WANG