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Book DetailsContemporary MathematicsCentre de Recherches Mathématiques ProceedingsVolume: 813; 2025; 351 ppMSC: Primary 17; 18; 57; 81
This volume contains the proceedings of the thematic program on “Quantum symmetries: Tensor categories, topological quantum field theories, and vertex algebras” held from October 10–November 4, 2022, at the Centre de Recherches Mathématiques, Montréal, Québec, Canada.
Quantum symmetries is a rapidly expanding area in which tensor categories are applied to mathematical physics, in particular, to conformal and topological quantum field theories. These fields, in turn, connect to a huge variety of modern mathematics, including representation theory, vertex operator algebras, Hopf algebras, link and knot invariants, geometry, subfactors, combinatorics, and so much more.
The thematic program on quantum symmetries featured advanced lecture courses and research seminars by international leaders of their respective fields. This proceedings volume is centered on the active research of the area, but also includes an in-depth survey of one of the main topics, \(W\)-algebras.
ReadershipGraduate students and research mathematicians interested in \(W\)-algebras, tensor categories and their applications in representation theory, and mathematical physics.
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Table of Contents
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Articles
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Jethro van Ekeren — Affine $W$-algebras
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Justine Fasquel — OPEs of rank two $W$-algebras
-
Andrew Riesen — Fusion rings acting on vertex operator algebras: First steps
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Alissa Furet and Theo Johnson-Freyd — Ground-state degeneracy of twisted sectors of Conway moonshine SCFT
-
Simon Lentner — Combinatorial principles that enforce a group structure
-
Eric C. Rowell, Hannah Solomon and Qing Zhang — On near-group centers and super-modular categories
-
Andrew Schopieray — Fixed-point-free fusion automorphisms
-
Theo Johnson-Freyd — $(3+1)D$ topological orders with only a $\mathbb {Z}_2$-charged particle
-
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert and Simon Wood — Grothendieck-Verdier duality in categories of bimodules and weak module functors
-
Christian Blanchet, Martin Palmer and Awais Shaukat — Action of subgroups of the mapping class group on Heisenberg homologies
-
Daniel Berwick-Evans, Emily Cliff, Laura Murray, Apurva Nakade and Emma Phillips — Flat principal 2-group bundles and flat string structures
-
Jin-Cheng Guu — Categorical center of higher genera
-
Joseph Vulakh — Twisted homogeneous racks over the alternating groups
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-
Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
This volume contains the proceedings of the thematic program on “Quantum symmetries: Tensor categories, topological quantum field theories, and vertex algebras” held from October 10–November 4, 2022, at the Centre de Recherches Mathématiques, Montréal, Québec, Canada.
Quantum symmetries is a rapidly expanding area in which tensor categories are applied to mathematical physics, in particular, to conformal and topological quantum field theories. These fields, in turn, connect to a huge variety of modern mathematics, including representation theory, vertex operator algebras, Hopf algebras, link and knot invariants, geometry, subfactors, combinatorics, and so much more.
The thematic program on quantum symmetries featured advanced lecture courses and research seminars by international leaders of their respective fields. This proceedings volume is centered on the active research of the area, but also includes an in-depth survey of one of the main topics, \(W\)-algebras.
Graduate students and research mathematicians interested in \(W\)-algebras, tensor categories and their applications in representation theory, and mathematical physics.
-
Articles
-
Jethro van Ekeren — Affine $W$-algebras
-
Justine Fasquel — OPEs of rank two $W$-algebras
-
Andrew Riesen — Fusion rings acting on vertex operator algebras: First steps
-
Alissa Furet and Theo Johnson-Freyd — Ground-state degeneracy of twisted sectors of Conway moonshine SCFT
-
Simon Lentner — Combinatorial principles that enforce a group structure
-
Eric C. Rowell, Hannah Solomon and Qing Zhang — On near-group centers and super-modular categories
-
Andrew Schopieray — Fixed-point-free fusion automorphisms
-
Theo Johnson-Freyd — $(3+1)D$ topological orders with only a $\mathbb {Z}_2$-charged particle
-
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert and Simon Wood — Grothendieck-Verdier duality in categories of bimodules and weak module functors
-
Christian Blanchet, Martin Palmer and Awais Shaukat — Action of subgroups of the mapping class group on Heisenberg homologies
-
Daniel Berwick-Evans, Emily Cliff, Laura Murray, Apurva Nakade and Emma Phillips — Flat principal 2-group bundles and flat string structures
-
Jin-Cheng Guu — Categorical center of higher genera
-
Joseph Vulakh — Twisted homogeneous racks over the alternating groups
