The goal of this online colloquium is to bring together postdocs and students associated to the Simons collaboration on Global Categorical Symmetries through talks accessible to an interdisciplinary audience. We hope to create a common vocabulary between mathematicians and physicists working on categorical symmetries, keep up with current developments in the field, and introduce the most important ideas and definitions. The colloquium is also supposed to strengthen the connection between the younger members of the collaboration and give them a place to discuss their (ongoing) research in an informal environment.
We will meet biweekly on Mondays, usually at 9am PT = 12pm ET = 6pm CET (modulo daylight savings).
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If you have any suggestions for speakers and/or topics to cover, submit your ideas using this google form.
During the 2024-2025 academic year, this colloquium series is organized by Sunghyuk Park (sunghyukpark@math.harvard.edu), Konstantinos Roumpedakis (kroumpedakis@gmail.com), and Pelle Steffens (pelle.steffens@tum.de). If you have any questions regarding the colloquium series, feel free to contact one of the organizers.
Upcoming meetings:
Previous meetings:
May 12, 2025 (Mon) at 4-5pm UTC (= 6-7pm CET = 12-1pm EST = 9-10am PST)
Speaker: Theo Jacobson (UCLA)
Title: Chiral boson at the edge of lattice Chern-Simons theory
Abstract: Regulating chiral quantum field theories on the lattice has been an outstanding problem since the inception of lattice gauge theory. In this talk, I describe a Hamiltonian lattice realization of the 1+1d chiral boson, which is one of the simplest examples of a chiral theory. This theory (both in the continuum and on the lattice) does not strictly speaking exist in isolation, but only as the boundary of a non-trivial topologically ordered 2+1d phase. I will show how to realize (Maxwell) Chern-Simons theory as a Hamiltonian lattice gauge theory, and show that it hosts a chiral edge mode on spatial lattices with boundary --- in essence, providing a lattice regularization of the fractional quantum hall effect.
Apr 14, 2025 (Mon) at 5-6pm UTC (= 7-8pm CEST = 1-2pm EDT = 10-11am PDT) *Note the different time from usual
Speaker: Severin Bunk (University of Hertfordshire)
Title: On higher symmetries in geometry
Abstract: Einstein gravity coupled to Yang-Mills theory is invariant under both spacetime diffeomorphisms and gauge transformations. However, these symmetries interact non-trivially, and the relevant symmetry group Sym(P) is a particular extension of the spacetime diffeomorphisms by the gauge transformations. For theories involving bundles whose structure group is a higher-categorical group, Sym(P) is itself a smooth higher group.
In this talk I will survey various applications of such groups of higher symmetries at the interface of geometry, topology and physics, ranging from magnetic monopoles over supergravity to differential cohomology. I will finish by sketching how infinitesimal versions of Sym(P) provide a unified approach to connections on higher-categorical bundles.
This is based on joint work with Lukas Müller, Joost Nuiten, Carlos Shahbazi, Richard Szabo and Vicente Muñoz.
Mar 31, 2025 (Mon) at 4-5pm UTC (= 6-7pm CET = 12-1pm EST = 9-10am PST)
Speaker: Francesco Mignosa (Oviedo U)
Title: String theory and the SymTFT of 3d ortho-symplectic ABJ theory
Abstract: Symmetries play a fundamental role in studying quantum field theories (QFTs). They provide selection rules, constrain the dynamics of QFTs, and, through anomalies, a method to test IR or UV dualities among different QFTs. For these reasons, it is important to understand the symmetries that a theory can enjoy. This recently motivated the study of generalized global symmetries and the description of symmetries through the symTFT, which separates the symmetry structure from the field theory dynamics. Holography represents a perfect laboratory to deal with these aspects: string theory reduced on the internal space of the holographic background realizes the symTFT and BPS branes describe the charged and topological operators of the dual theory. In this talk, I will focus on the type IIA description of ABJ theories. These are an interesting topic in this context: one of their global forms enjoys a binary dihedral or quaternionic discrete symmetry depending on their rank and CS levels, and their holographic dual is known. After characterizing the symmetry web of these theories, I will describe the symTFT and its topological operators, in particular focusing on non-genuine operators showing how the non-Abelian structure of the symmetry group can be detected from their fusion rules and commutation relations. I will then focus on the holographic realization of the theory, obtaining the symTFT from type IIA supergravity. I will identify symmetry operators in terms of BPS branes and see how their tadpoles encode the group structure of the global symmetry. Finally, I will comment on the realization of non-invertible genuine operators through branes, computing the attached TQFT from the reduction of the brane worldvolume theory on the cycle the brane is wrapping. Based on an upcoming work with O. Bergman.
Feb 3, 2025 (Mon) at 2:30-3:30pm UTC (= 3:30-4:30pm CET = 9:30-10:30am EST = 6:30-7:30am PST)
Speaker: Ho Tat Lam (MIT)
Title: Dynamical Constraints from Projective Non-invertible Symmetries
Abstract: 't Hooft anomalies of global symmetries impose powerful constraints on the dynamics of a quantum system. In this talk, I will begin by reviewing 't Hooft anomalies associated with projective unitary symmetries in quantum lattice models, which gives rise to the celebrated Lieb-Schultz-Mattis (LSM) theorem that rules out a unique gapped ground state. Next, I will introduce non-invertible symmetries based on a concrete lattice model. Surprisingly, I will show how projective non-invertible symmetries do not always exhibit 't Hooft anomalies and, therefore, do not necessarily imply an LSM theorem. However, even in such cases, a weaker dynamical constraint still holds, giving rise to an SPT-LSM theorem: any unique gapped ground state is necessarily a non-invertible weak symmetry-protected topological state with non-trivial entanglement.
Mar 3, 2025 (Mon) at 5-6pm UTC (= 6-7pm CET = 12-1pm EST = 9-10am PST)
Speaker: Giovani Galati (Brussels U)
Title: Flat Gauging, Compact Boson & T-duality
Abstract: The free theory of a single compact boson in 2d is a paradigmatic example of a solvable theory, exhibiting extremely interesting features and a rich symmetry structure. In this talk, I will explain how, by allowing for peculiar topological manipulations—such as gauging continuous symmetries with flat connections—one can derive many of these features, including the existence of a conformal manifold and a non-invertible T-duality symmetry that generalizes the well-known one appearing at rational values of the squared radius. Finally, I will show how all these properties are nicely encoded in the Symmetry TFT description of the theory.
Dec 9, 2024 (Mon) at 5-6pm UTC (= 6-7pm CET = 12-1pm EST = 9-10am PST)
Speaker: Nikita Sopenko (IAS)
Title: An index for 2d invertible phases of quantum many-body systems
Abstract: I will discuss the classification of phases of quantum many-body systems at zero temperature in two dimensions. Under favorable circumstances, the edge modes of such systems can be described by a 1+1d conformal field theory. It is believed that the chiral central charge c_- of the theory is a robust characteristic of the phase that can be defined even when conformal symmetry is not present on the boundary, and there is no effective field theory description. In the talk, I will discuss a microscopic definition of the invariant c_- mod 24 for invertible phases. This invariant provides a generalization of the Chern number for gapped free fermionic systems to the interacting setting.
Nov 25, 2024 (Mon) at 5-6pm UTC (= 6-7pm CET = 12-1pm EST = 9-10am PST)
Speaker: Bowen Yang (Harvard CMSA)
Title: Bulk-Boundary correspondence for stabilizer codes
Abstract: Translation-invariant stabilizer codes is an important class of exactly solvable models. They admit an elegant mathematical formulation in terms of modules over a group ring. Under the transformation of Clifford QCA, certain `topological charges’ remain invariant and computable through homological algebra. We explain these invariants in the bulk on the one hand, but demonstrate, on the other hand, their tractability over the boundary. Time permitting, I’ll characterize the system where these ‘topological charges’ vanish.
Nov 4, 2024 (Mon) at 3-4pm UTC (= 4-5pm CET = 10-11am EST = 7-8am PST) *Note the different time from usual
Speaker: Dmitry Solovyev (YMSC)
Title: Towards $\hat{Z}$ from $q6j$-symbols for Verma modules
Abstract: The talk is based on arXiv:2410.18463. The shadow world is a graphical representation for quantum 6j-symbols of finite-dimensional representations of $U_q(sl_2)$. It provides a model for the colored Jones polynomial, which is equivalent to the model coming from the R-matrix. It is known that the R-matrix approach for Verma modules of $U_q(sl_2)$ reproduces Gukov-Manolescu series. This talk is devoted to the study of Gukov-Manolescu series from the perspective of the shadow world, which gives hints on a possible target category for the Reshetikhin-Turaev functor for $\hat{Z}$.
2:00-4:00 PM (UTC) May 20 2024 (Topic: Defect CFTs and Tensor Networks):
- Avia Raviv, Line Defects in CFTs: from Magnets and Impurities to Wilson Lines
- Pranay Gorantla, Non-invertible duality symmetries using tensor networks
1:00-3:00 PM (UTC) April 15 2024 (Topic: LSM anomalies and gauging on the lattice):
- Ömer Mert Aksoy, From Lieb-Schultz-Mattis Theorems to Anomalies with Crystaline Symmetries
- Sahand Seifnashri, Non-invertible lattice translation symmetries and LSM anomalies
3:00-5:00 PM (UTC) March 18 2024:
- Xingyang Yu, Stringy Approach to Categorical Symmetries
- Giovanni Galati, Research Talk: Exploring Duality Symmetries, Multicriticality, and RG Flows at c=2
3:00 - 5:00 PM (UTC) February 19 2024 (Topic: Non-semisimple fully extended skein TQFTs):
- Lukas Müller, Background Talk: An introduction to Skein Theory
- Luuk Stehouwer, Background Talk: The Cobordism Hypothesis: A Computational Approach to TQFTs
- Benjamin Haioun, Research Talk: Non-semisimple fully extended skein TQFTs
12:00 AM - 2:00 PM (UTC) December 18 2023 (Topic: Higgs branches and their categorical properties):
- Zhenghao Zhong, Research Talk: Magnetic Quivers and the Radioactive Higgs Mechanism
- Veronica Pasquarella, Research Talk: Moore-Tachikawa Varieties: Beyond Duality
3:00 - 5:00 PM (UTC) November 20 2023 (Topic: Defects in TQFTs):
- Jenny Brown, Research talk: Defects in Skein Theory
- Wenjun Niu, Research talk: Kazhdan-Lusztig correspondence for a class of Lie superalgebras
2:00 - 4:00 PM (UTC) October 23 2023:
- Andrea Antinucci & Giovanni Rizi, Background talk: An introduction to holographic approach to symmetry
- Azeem Hasan, Research talk: Class S and geometric origin of its non-invertible symmetries
3:00 - 5:00 PM (UTC) May 22 2023 (Topic: Factorization algebras):
- Araminta Amabel, Background talk: Factorization Algebras of Observables
- Chris Elliott, Research talk: Framing Anomalies and Kapustin-Witten Theory
3:00 - 5:00 PM (UTC) April 24 2023:
- Jackson Van Dyke & Will Stewart, Background talk: Topological symmetries and the Drinfeld center
- Andrea Grigoletto, Research talk: Representation theory for categorical symmetries
3:00 - 5:00 PM (UTC) March 20 2023:
- Héctor Martín Peña Pollastri, Research talk: Hopf algebras, quantum groups, an approach to classification and new examples
- Iordanis Romaidis, Research talk: Mapping class group actions and rational CFT
3:00 - 5:00 PM (UTC) February 27 2023:
- Anuj Apte, Research Talk: Non-invertible Symmetry Enforced Gaplessness
- Po-Shen Hsin, Research Talk: Higher group symmetry and finite group gauge theory
3:00 - 5:00 PM (UTC) January 23 2023:
- Arun Debray & Matthew Yu, Background talk on anomalies
- Diego Delmastro, Research talk: Anomalies and all that stuff
3:00 - 5:00 PM (UTC) December 12 2022:
- Saghar Sophie Hosseini, Background talk: Geometric engineering of quantum field theories and symmetries from string theory
- Sunghyuk Park, Research talk: 3-manifolds and q-series
3:00 - 5:00 PM (UTC) November 14 2022:
- Thibault Dekoppet & Sean Sanford, Background talk: Morita Theory of (Higher) Fusion Categories: Intro and Examples
- Eilind Karlsson, Research talk: Higher Morita categories and dualizability