GLOBAL CATEGORICAL SYMMETRIES 2026

15 juin 2026, 09:00 → 3 juil. 2026, 18:00 Europe/Paris

Institut Henri Poincaré

Thematic 3-weeks programme at the Institut Henri Poincaré, Paris, June 15th to July 3rd, 2026.

Beware: It was reported to us that scammers are sending to participants fraudulent e-mails about accomodation/fees. Please be particularly cautious about e-mails not coming from the organisers nor from an @ihp.fr address. 

Abstract

Some of the most profound open problems about the physics of quantum fields – especially at strong coupling, beyond the reach of conventional techniques – are newly accessible thanks to recent developments in topological quantum field theory (TQFT). This insight comes with a dramatic evolution of the notion of symmetries in QFT: symmetries can be characterized via topological defects of various codimensions whose multidimensional fusion generalizes wildly the notion of groups to what are called categorical symmetries. This IHP program is the fourth in a series of meetings hosted at various institutes worldwide devoted to the exploration of these aspects of symmetries, the resulting mathematical structures and their physical implications, in the context of the Simons Collaboration on Global Categorical Symmetries. World-class experts in the subject will gather at IHP in an interactive setting alternating lectures and seminars aiming at nourishing collaborations and stimulate further this rapidly evolving field.

During the first week of this program we invite PhD students and postdocs to the fourth GCS summer school. Support is available for those who apply. During the second week of this program we will host the conference Symmetries 2026, an international gathering of experts where the most recent developments about this topic will be presented. The third week of this program is a smaller workshop, where groups of researchers are welcome to network and develop new projects and ideas. More information will appear on this webpage closer to the event.

 

The program unfolds over three weeks: a school, a conference, and finally a workshop.

June 15-19: GCS26 School

IHP, Amphithéâtre Hermite, Borel Building

Lecturers

Agnès Beaudry (Colorado U Boulder)

Federico Bonetti (Murcia U)

Nat Tantivasadakarn (YITP, Stony Brook U)

Tomer Schlank (Chicago U)

Yifan Wang (NYU)

June 22-26: Symmetries 26 Conference 

IHP, Amphithéâtre Hermite, Borel building

Speakers

Andrea Antinucci (Oxford U)

Lea Bottini (IHES)

Adrien Brochier (Paris Cité)

Damien Calaque (U de Montpellier)

Christian Copetti (Oxford U)

Clay Córdova (Chicago)

Arun Debray (Kentucky U)

Thibault Decoppet (Harvard U)

Lukasz Fidkowski (Seattle U)

Jonathan Heckman (UPenn)

Wenjie Ji (PI)

Anton Kapustin (Caltech)

Cameron Krulewski (DAL)

Enoch Leung (LMU)

John McGreevy (UCSD)

Lukas Müller (PI)

Nivedita (Oxford U)

Salvatore Pace (MIT - IAS)

Julio Parra-Martinez (IHES)

Brandon Rayhaun (IAS)

David Reutter (Hamburg U)

Sakura Schafer-Nameki (Oxford U)

Pelle Steffens (TUM)

Xiao-Gang Wen (MIT)

Carolyn Zhang (Harvard U)

Yunqin Zheng (KIST-UCIS)

Chenchang Zhu (Göttingen U)

June 29-July 3: GCS26 workshop

IHP, Amphithéâtre Darboux, Borel building

 

Registration is free but mandatory.
Deadline for asking financial support: February 15th, 2026. 
Financial support is limited and will be notified by March 15th, 2026. 
Places are limited.

 

Organising committee:

• Ibrahima Bah (John Hopkins University)
• Michele Del Zotto (Uppsala University) 
• Theo Johnson Freyd (Dalhousie University & Perimeter Institute) 
• Ruben Minasian (CEA Saclay)
• Claudia Scheimbauer (TU Munich)

 

Scientific committee:

• Thomas Dumitrescu (University of California Los Angeles)
• Dan Freed (University of Texas)
• Constantin Teleman (University of California Berkley)

 

Fundings: 

The program receives also support from:

Simons Collaboration on Global Categorical Symmetries

Official_Poster_GCS2026 NEW.pdf

lun. 15 juin

09:00 → 10:30 Beaudry: From Stabilizer Codes to Fracton Phases of Matter

Fracton orders are quantum systems characterized by the presence of excitations with restricted mobility. Many examples are described by stabilizer codes, that is, lattice Hamiltonians constructed from commuting generalized Pauli matrices. In this lecture series, we will explore the algebraic framework for fracton phases and mutual statistics that emerges from the study of stabilizer codes.

The course will be mostly based on work of Haah and Ruba-Yang, as well as joint work with Hermele, Shirley, Wickenden and Yang.

Paris - Lectures - Final.pdf

10:30 → 11:00 Coffee break

11:00 → 12:30 Wang: Seeing through Defects in Quantum Field Theory

Defects provide powerful probes of quantum field theory. Supported on lower-dimensional subspaces, they host their own degrees of freedom, generalize ordinary local operator algebras, and exhibit novel phases connected by renormalization group flows. We will discuss modern developments in defect dynamics, focusing on their interplay with symmetries and anomalies, and explain how they encode structural information about the ambient QFT.

12:30 → 14:30 Lunch break

Lunch is not provided. Plenty of options for lunch are available nearby.

14:30 → 16:00 Wang: Seeing through Defects in Quantum Field Theory

Defects provide powerful probes of quantum field theory. Supported on lower-dimensional subspaces, they host their own degrees of freedom, generalize ordinary local operator algebras, and exhibit novel phases connected by renormalization group flows. We will discuss modern developments in defect dynamics, focusing on their interplay with symmetries and anomalies, and explain how they encode structural information about the ambient QFT.

mar. 16 juin

09:00 → 10:30 Beaudry: From Stabilizer Codes to Fracton Phases of Matter

Fracton orders are quantum systems characterized by the presence of excitations with restricted mobility. Many examples are described by stabilizer codes, that is, lattice Hamiltonians constructed from commuting generalized Pauli matrices. In this lecture series, we will explore the algebraic framework for fracton phases and mutual statistics that emerges from the study of stabilizer codes.

The course will be mostly based on work of Haah and Ruba-Yang, as well as joint work with Hermele, Shirley, Wickenden and Yang.

10:30 → 11:00 Coffee break

11:00 → 12:30 Wang: Seeing through Defects in Quantum Field Theory

Defects provide powerful probes of quantum field theory. Supported on lower-dimensional subspaces, they host their own degrees of freedom, generalize ordinary local operator algebras, and exhibit novel phases connected by renormalization group flows. We will discuss modern developments in defect dynamics, focusing on their interplay with symmetries and anomalies, and explain how they encode structural information about the ambient QFT.

12:30 → 14:30 Lunch break

Lunch is not provided. Plenty of options for lunch are available nearby.

14:30 → 16:00 Tantivasadakarn: Symmetries and their gauging on the lattice

Much progress of generalized symmetries has been formulated in the continuum. However, on the lattice, symmetries can behave quite differently, and its fundamental organizing principles are still in development. I will give a broad introduction to symmetries on the lattice and how to gauge them. Time permitting, I will discuss subtleties in matching symmetries on the lattice to those in the continuum.

mer. 17 juin

09:00 → 10:30 Beaudry: From Stabilizer Codes to Fracton Phases of Matter

Fracton orders are quantum systems characterized by the presence of excitations with restricted mobility. Many examples are described by stabilizer codes, that is, lattice Hamiltonians constructed from commuting generalized Pauli matrices. In this lecture series, we will explore the algebraic framework for fracton phases and mutual statistics that emerges from the study of stabilizer codes.

The course will be mostly based on work of Haah and Ruba-Yang, as well as joint work with Hermele, Shirley, Wickenden and Yang.

10:30 → 11:00 Coffee break

11:00 → 12:30 Schlank: intro to stable Homotopy theory with a view towards quantum field theory

In this series of talks I will give an introduction to the the subject of stable Homotopy theory,

We shall discuss spectra, higher algebra, chromatic homotopy and other fundamental notion of this theory.

12:30 → 14:30 Lunch break

Lunch is not provided. Plenty of options for lunch are available nearby.

14:30 → 16:00 Bonetti: Aspects of SymTFT and Continuous Symmetries

In the modern perspective, the generalized global symmetries of a quantum field theory (QFT) are encoded in the spectrum of its (extended) topological operators. Finite symmetries, in particular, are expected to be captured by higher fusion categories. The Symmetry Topological Field Theory (SymTFT) provides a powerful framework for analyzing many facets of these symmetry structures.

While categorical methods and SymTFT techniques are by now well established for finite symmetries, a complete and systematic framework for continuous symmetries is still being developed. In these lectures, I will present some features of SymTFTs for continuous symmetries from a physicist’s perspective. As a complementary approach to better understanding the properties of symmetry operators associated with continuous symmetries, I will also discuss aspects of their realization in holography and string theory.

16:00 → 18:00 Poster session + Coffee break

18:15 → 21:00 Cocktail diner party @Les Cordeliers - Salle Marie Curie - 15, rue de l’école de médecine

jeu. 18 juin

09:00 → 10:30 Tantivasadakarn: Symmetries and their gauging on the lattice

Much progress of generalized symmetries has been formulated in the continuum. However, on the lattice, symmetries can behave quite differently, and its fundamental organizing principles are still in development. I will give a broad introduction to symmetries on the lattice and how to gauge them. Time permitting, I will discuss subtleties in matching symmetries on the lattice to those in the continuum.

10:30 → 11:00 Coffee break

11:00 → 12:30 Schlank: intro to stable Homotopy theory with a view towards quantum field theory

In this series of talks I will give an introduction to the the subject of stable Homotopy theory,

We shall discuss spectra, higher algebra, chromatic homotopy and other fundamental notion of this theory.

12:30 → 14:30 Lunch break

Lunch is not provided. Plenty of options for lunch are available nearby.

14:30 → 16:00 Bonetti: Aspects of SymTFT and Continuous Symmetries

In the modern perspective, the generalized global symmetries of a quantum field theory (QFT) are encoded in the spectrum of its (extended) topological operators. Finite symmetries, in particular, are expected to be captured by higher fusion categories. The Symmetry Topological Field Theory (SymTFT) provides a powerful framework for analyzing many facets of these symmetry structures.

While categorical methods and SymTFT techniques are by now well established for finite symmetries, a complete and systematic framework for continuous symmetries is still being developed. In these lectures, I will present some features of SymTFTs for continuous symmetries from a physicist’s perspective. As a complementary approach to better understanding the properties of symmetry operators associated with continuous symmetries, I will also discuss aspects of their realization in holography and string theory.

ven. 19 juin

09:00 → 10:30 Tantivasadakarn: Symmetries and their gauging on the lattice

Much progress of generalized symmetries has been formulated in the continuum. However, on the lattice, symmetries can behave quite differently, and its fundamental organizing principles are still in development. I will give a broad introduction to symmetries on the lattice and how to gauge them. Time permitting, I will discuss subtleties in matching symmetries on the lattice to those in the continuum.

10:30 → 11:00 Coffee break

11:00 → 12:30 Schlank: intro to stable Homotopy theory with a view towards quantum field theory

In this series of talks I will give an introduction to the the subject of stable Homotopy theory,

We shall discuss spectra, higher algebra, chromatic homotopy and other fundamental notion of this theory.

12:30 → 14:30 Lunch break

Lunch is not provided. Plenty of options for lunch are available nearby.

14:30 → 16:00 Bonetti: Aspects of SymTFT and Continuous Symmetries

In the modern perspective, the generalized global symmetries of a quantum field theory (QFT) are encoded in the spectrum of its (extended) topological operators. Finite symmetries, in particular, are expected to be captured by higher fusion categories. The Symmetry Topological Field Theory (SymTFT) provides a powerful framework for analyzing many facets of these symmetry structures.

While categorical methods and SymTFT techniques are by now well established for finite symmetries, a complete and systematic framework for continuous symmetries is still being developed. In these lectures, I will present some features of SymTFTs for continuous symmetries from a physicist’s perspective. As a complementary approach to better understanding the properties of symmetry operators associated with continuous symmetries, I will also discuss aspects of their realization in holography and string theory.

lun. 22 juin

09:00 → 09:05 Opening Remarks

Orateur: Mariana Grana (Institut Henri Poincare)

09:05 → 09:45 McGreevy: Entanglement Bootstrap and Symmetric Conformal Field Theories

Entanglement Bootstrap is a research program to understand and extract the universal data of quantum many body states from local entanglement information. The program proceeds by identifying conditions satisfied by the reduced density matrix of a ball for a given class of fixed-point states. I'll describe our progress at using this philosophy to learn about the space of conformal field theories in 1+1 dimensions and above, and how it can be refined by the imposition of symmetries. The talk is based on work with Xiang Li, Ting-Chun (David) Lin, and Rolando Ramirez Camasca.

2026-06-22-MCGREEVY.pdf

09:50 → 10:30 Fidkowski: Chiral Lattice gauge theories from symmetry disentanglers

We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers: constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for U (1) symmetries with mixed ’t Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional “3450” chiral gauge theory, and we argue that a related construction applies to the U (1) hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories.

IHES_2026_pdf.pdf

10:35 → 11:05 Coffee break

11:05 → 11:45 Córdova: Holomorphic CFT and Modular Tensor Categories

We study the interplay between holomorphic conformal field theory and dualities of 3d topological quantum field theories generalizing the paradigm of level-rank duality. A holomorphic conformal field theory with a Kac-Moody subalgebra implies a topological interface between Chern-Simons gauge theories. Upon condensing a suitable set of anyons, such an interface yields a duality between topological field theories. We illustrate this idea using the c = 24 holomorphic theories classified by Schellekens, which leads to a list of novel sporadic dualities. Some of these dualities necessarily involve condensation of anyons with non-abelian statistics, i.e. gauging non-invertible one-form global symmetries. Several of the examples we discover generalize from c = 24 to an infinite series.

GCS_Cordova.pdf

11:50 → 12:30 Wen: Chiral U(1) higher gauge theory and associated chiral (higher) U(1) anomaly on spacetime lattice

I will discussion how to put chiral U(1) higher gauge theories (such as Chern-Simons theory) on spacetime lattice.
This gives us lattice model with chiral (higher) U(1) anomaly that has no gapped phases, without explicitly breaking the U(1) symmetry.

Wen-260622-GCS-IHP.pdf

12:35 → 14:30 Lunch break

Lunch is not provided. Plenty of options for lunch are available nearby.

14:30 → 15:10 Zhang: Spontaneous symmetry breaking in non-equilibrium dynamics

We present simple toy models of mixed state phases and phase transitions beyond thermal transitions, observed from the steady state structure of strongly symmetric local Lindbladians. To diagnose these mixed state phases and study phase transitions, we introduce a local order parameter that can be computed efficiently to obtain critical exponents.

Symmetries 2026 Paris pdf.pdf

15:15 → 15:55 Leung: Basepoint anomalies and the vanishing of partition functions

We discuss a sufficient (but not necessary) condition for partition functions of QFTs to vanish, meaning that generic correlators are zero unless suitable operators are inserted. Vanishing partition functions have been observed in multiple occasions in the past. Here we provide a systematic perspective from the moduli space to unify these seemingly independent results. In the context of D-branes, we recover the Freed-Witten anomaly cancellation condition, and our approach allows us to extend it to branes in non-perturbative string/M-theory backgrounds.

Leung.pdf

16:00 → 18:00 Poster session + wine and cheese

mar. 23 juin

08:15 → 08:55 Krulewski: Invertible Field Theories and the Bott Spiral

Reflection-positive fully extended invertible field theories on manifolds with twisted spin structures provide homotopical classifications for fermionic SPTs. Free fermion SPTs, a subset, are classified by K-theory. Generalizing work of Freed--Hopkins, we define and compute homotopical "free-to-interacting maps" between these classifications for the special case of the "Bott spiral" of SPTs studied originally by Queiroz--Khalaf--Stern. Time permitting, I will discuss some subtleties of our construction, such as compatibility with dimensional reduction, continuous versus discrete symmetry types, and the lack of interacting Morita invariance.

GCS Paris 2026 - Bott Spiral v4.pdf

09:00 → 09:40 Kapustin: Higher symmetries and homotopy theory in quantum lattice models

It is generally accepted that the interplay of symmetry and locality in Quantum Field Theory leads one to introduce higher or generalized symmetries. While ordinary (0-form) symmetries form a group, incorporating invertible higher symmetries requires one to replace groups with higher groups, that is, finite connected homotopy types. It is far from obvious how to attach such a gadget to a local QFT. In this talk I discuss this problem in the context of quantum lattice models. I will show how to attach a connected homotopy (d+1)-type to lattice models in d spatial dimensions by exploiting a construction which is a non-abelian analog of the Cech homology of a precosheaf. This homotopy type encodes all higher symmetries as well as all 't Hooft anomalies. A key ingredient in the construction is the equivalence between connected homotopy (d+1)-types and crossed d-cubes of groups due to Loday and Ellis-Steiner.

09:45 → 10:25 Copetti: When Symmetries Twist - Anomaly inflow on Monodromy Defects

Symmetries can constrain exactly properties of dynamical defects. In this talk I will focus on Monodromy defects, which describe dynamical terminations of the symmetry operators themselves. I will review how they provide natural detectors of nontrivial disordered phases (SPTs), and employ anomaly inflow to then derive exact constraints on their physical properties in anomalous gapless theories.

sym26.pdf

10:30 → 10:55 Coffee break

10:55 → 11:35 Zhu: Towards Weinstein's category for shifted symplectic structures via groupoids

Under the motto that “everything is Lagrangian”, Alan Weinstein proposed a category whose objects are symplectic manifolds and whose morphisms are Lagrangian correspondences. As Poisson geometry has developed over the past decades—motivated largely by classical mechanics—additional structures such as Poisson, Dirac, and Courant have emerged. Safronov, drawing on the shifted symplectic structures of Pantev–Toën–Vaquié–Vezzozi (PTVV), places these geometric structures into a unified framework by viewing them as symplectic structures of various shifts.

The quantization of 1-shifted symplectic geometry, as developed through Meinrenken’s work and the Freed–Hopkins–Teleman theorem, naturally takes values in twisted K-theory and K-homology, and in particular in the Verlinde ring. In this sense, shifted symplectic geometry provides not only a conceptual framework for Poisson-type structures, but also a geometric counterpart to K-theoretic and representation-theoretic invariants.
Calaque-Haugseng-Scheinbauer constructed a TFT with target a version of such Weinstein category for shifted symplectic structures using higher derived stacks in the sense of Toën–Vezzosi. While the language of stacks is intrinsic, it remains rather implicit for differential geometers and therefore difficult to use for concrete calculations. Pridham approaches higher derived stacks via presentations by groupoids, a setting far more familiar to researchers in differential geometry, dynamical systems, and noncommutative geometry. E.g. in nummeric Hamiltonian systems, explicit symplectic groupoids were in need to construct Poisson integrator.

Inspired by Pridham’s approach, we work towards a Weinstein category for shifted symplectic structures using higher derived Lie groupoids. However, the topology we use for derived manifolds differs from that of Toën–Vezzosi and Pridham: we work with fibrations admitting local sections, which allow us to treat the odd line and cotangent groupoids—key examples in Poisson geometry.

We prove that when intersections are transversal in a higher derived sense, the composition of Lagrangian correspondences remains Lagrangian. As always, there is technical difficulty when intersection is not transversal. Broadly, two methods are available: (1) perturbation, as in the Fukaya category, which yields explicit results but requires delicate analysis; or (2) (fibrant) replacement, as in PTVV, which is conceptual but requires a homotopical framework and typically leaves explicit fibrant replacements to be worked out.

We take the second approach and build an iCFO (incomplete category of fibrant objects) for derived higher Lie groupoids and provide explicit fibrant replacements using a collection of tubular neighborhood theorems: Weinstein’s Lagrangian tubular neighborhood theorem, and the Hoyo–Fernandes version for Lie groupoids via the Crainic–Fernandes–Torres PMCT program. As applications, we use Calaque–Safronov’s trick, then singular symplectic reduction, quasi-symplectic reduction, and Lu–Weinstein reduction, all appear as shifted symplectic derived Lie groupoids. This is based on a joint work in progress with M. Cueca, F. Dorsch, and R. Sjamaar.

Weinstein category for shifted symplectic structures via grouppid.pdf

11:40 → 12:20 Debray: What are the possible anomalies of four-dimensional topological field theories?

What are the possible anomalies of four-dimensional topological field theories?
Abstract: Whether a given quantum field theory (QFT) can be approximated by a topological field theory (TFT) at long distances is an important qualitative aspect of the QFT. Since the anomaly of a QFT is invariant under such an approximation, we can attack this question by asking, "of all possible anomalies, which ones are anomalies of TFTs?", which is a rigorous mathematical question. In joint work with Weicheng Ye and Matthew Yu, we solve this question for four-dimensional Spin x_{\pm 1} G TFTs: the bottommost layer of the Atiyah--Hirzebruch spectral sequence is a complete obstruction to being the anomaly of a TFT. Moreover, when this obstruction vanishes, there is an algorithmic construction of a TFT realizing the anomaly. Our work builds on Décoppet--Yu's symmetry extension construction for fusion 2-categories as well as Córdova--Ohmori's answer to this question for cyclic G.

paris.pdf

mer. 24 juin

07:30 → 08:10 Decoppet: The Classification of 3+1d Symmetry Enriched Topological Order

I will show that a 2-categorical version of (de-)equivariantization can be used to classify (3+1)d topological orders with a finite G-symmetry.
As a consequence, in the genuinely fermionic case, I will explain how the categorical data necessary to define these theories agrees with that arising from a fermionic generalization of the Wang-Wen-Witten construction of bosonic topological theories with G-symmetry saturating an anomaly. This is joint work with Matthew Yu.

08:15 → 08:55 Calaque: A discrete 1d TFT with a point defect

I will start by recalling a general result, obtained together with Victor Carmona (Leipzig), about "algebras over not too little disks". I will then illustrate this result in dimension 1, using a construction (of a discrete 1d TFT on the line with a point defect) from a work in progress that is joint with Maziar Farahzad (Toronto). I will finally explain how this construction in particular recovers the well-known quantization of linear coisotropic reduction.

CalaqueDiscreteTFT.pdf

09:00 → 09:40 Brochier: Swiss-Cheese, Poisson groups and topology

As observed by many authors, the theory of finite-dimensional Poisson
algebraic groups and of their quantizations has a natural interpretation
in terms of 2d TFTs equipped with a pair of transverse boundary
conditions. There are then various dualities in this theory which are
reflected in symmetries of the associated TFT. In this talk we'll give
an overview of this approach with an eye toward applications in
low-dimensional topology. One of our main motivation was to understand
the work of Alekseev--Enriquez--Torrossian and of Bar-Natan--Dancso
which shows a surprising connection between the Kashiwara-Vergne
conjecture and the Duflo isomorphism in Lie theory, and the braid groups
actions on character varieties of punctured discs.

brochier.pdf

09:45 → 10:15 Coffee break

10:15 → 10:55 Bottini: Topological order enriched by non-invertible symmetry via anyon condensation

In this talk, I will discuss a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order, a well-established formalisation is available in terms of a G-crossed braided fusion category. By considering the condensation of an arbitrary algebra of charges in a quantum double model, a generalisation of this framework naturally emerges. In particular, I will show the topological order after condensation can be described as a hypergroup-graded extension of the category of deconfined excitations. This has a hypergroup symmetry which acts in a typically non-invertible manner on the confined and deconfined excitations in a way that is compatible with the grading. I will illustrate the general theory through a simple example.

Paris talk.pdf

11:00 → 11:40 Rayhaun: Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras

There is by now a beautiful theory of generalized symmetries for 2D QFTs based in the physics of topological line defects and the mathematics of tensor categories. I will sketch a generalization of this theory to the setting of relative 2D QFTs (i.e. QFTs which live at the boundary of a bulk 3D topological order), emphasizing various new algebraic structures that arise, such as hypergroups. This theory is particularly rich when applied to the chiral half of a CFT, and I will spend most of the time unpacking this special case and discussing applications.

11:45 → 12:25 Antinucci: A Twist on Scattering from Defect Anomalies

Scattering processes involving particles and very heavy probes, modeled by defects, have recently been shown to exhibit an unexpected feature: radiation can be emitted into twisted sectors rather than into the ordinary Hilbert space. In this talk, I will explain that the underlying mechanism is rooted in the subtle realization of bulk symmetries in the presence of defects. In particular, certain defect ’t Hooft anomalies allow charge to be trapped on the defect during scattering, thereby opening channels that would otherwise be forbidden by conservation laws. This viewpoint provides a systematic way to predict the phenomenon in new settings, including massive theories. I will present the general mechanism and discuss explicit examples in 1+1 dimensions.

jeu. 25 juin

07:30 → 08:10 Ji: Self-dual Higgs transitions: Toric code and beyond

In (2+1)d, the transition from the Z_2 toric code phase to a trivial phase can be driven by the condensation of either the electric anyon e or magnetic anyon m. When the system has a global Z_2 “self-duality” symmetry that exchanges e and m anyons, the naive anyon-condensation picture no longer holds since e and m cannot simultaneously condense. Numerical studies have found a continuous transition from the toric code with the Z_2 self-duality symmetry to a trivial phase with the Z_2 spontaneously broken. Since then, a natural field-theoretic understanding of this transition has remained an open challenge. In this talk, I will propose an SO(4) Chern-Simons-Higgs (CSH) theory at level k=2 as a natural mean-field description of this self-dual transition. I will further show that varying the integer level k gives a broader series of analogous transitions involving non-Abelian topological orders, including the double Fibonacci order at k=3 and the S_3 quantum double at k=4.

https://arxiv.org/abs/2601.20945

2026_GCS_IHP.pdf

08:15 → 08:55 Zheng: Non-invertible Symmetries in Weyl Fermions, and Applications to Fermion-Boundary Scattering Problem

We discuss a family of non-invertible topological defects in two-dimensional theories of n Weyl fermions. The construction relies on the existence of G-symmetric conformal boundary conditions for nDirac fermions. Upon unfolding, these boundary conditions become topological defects D of n Weyl fermions that intertwine the two G-representations, and they are generically non-invertible. We illustrate this construction when G= U(1)^n, where the topological defect D can be shown to be a duality defect associated with gauging certain finite abelian group Γ. By contrast, for certain non-Abelian symmetry including the G= SU(2) symmetry appearing in the 1-5-7-8-9 problem, we prove that D cannot be realized as a duality defect for gauging any finite Abelian group. We explain how the duality-defect perspective can be used to re-derive the fermion scattering from a conformal boundary.

Paris 06252026.pdf

09:00 → 09:40 Pace: Infinite-order lattice anomalies and CPT

A key property of a global symmetry's anomaly is its order: the smallest integer n for which the diagonal symmetry of the n-copy system is anomaly-free.
While many familiar lattice anomalies have finite order, perturbative anomalies in the continuum—those captured by Feynman diagrams—have infinite order.
In this talk, we show that the Onsager symmetry, a lattice realization of the chiral symmetry of a 1+1d massless Dirac fermion, has an order-two anomaly.
However, imposing lattice CPT symmetry enhances this anomaly from order two to infinite order, yielding a lattice chiral symmetry structure that more faithfully matches the continuum chiral anomaly. (This talk is based on arXiv:2606.12510 with Elijah Lew-Smith and Shu-Heng Shao.)

Pace_Symmetry26.pdf

09:45 → 10:15 Coffee break

10:15 → 10:55 Nivedita: Constructing fully extended functorial Chiral CFTs

Two-dimensional unitary chiral conformal field theories (CFTs) admit three distinct mathematical formulations: unitary vertex operator algebras (uVOAs), conformal nets, and Segal (functorial) chiral CFTs. With the aim of building a fully extended functorial chiral CFT from the data of a conformal net, we give its values on points and 1-dimensional cobordisms: to a point, we assign the category of solitonic representations of the net, and to a 1-dimensional cobordism, a bimodule category. We then prove that this assignment is functorial, with gluing of cobordisms corresponding to fusion of modules. The algebraic target of the construction is the 3-category BicomCat of bicommutant categories, the functional-analytic analogue of TensCat. We introduce the fusion of modules over bicommutant categories as 'categorified' Connes fusion.

Slides GCS_Nivedita .pdf

11:00 → 11:40 Alison Warman: Intrinsic DQCP Transitions from Twin Phases

We introduce the concept of twin phases for a symmetry S, defined as inequivalent phases, whose order parameters are part of the same generalized charge under S. Stable, direct transitions between such twin phases are never spontaneous-symmetry-breaking transitions, even after (partially) gauging the initial symmetry S: they are phase transitions without hidden symmetry breaking. We illustrate this with an (anomalous) finite group symmetry in 1+1d, which exhibits such intrinsically beyond Landau DQCP transitions.
This is based on work with Alison Warman and Yuhan Gai.

Paris_Twin_Phases.pdf

ven. 26 juin

07:30 → 08:10 Reutter: A higher category of topological quantum field theories

It is commonly expected that n-dimensional topological quantum field theories and their interfaces assemble into an n-category.
In this talk, I will suggest a list of reasonable assumptions satisfied by such an n-category of (discrete and semisimple) TQFTs, including Freed and Hopkins’ suggestion that invertible theories are completely determined by their partition functions on closed manifolds. I will then explain that there is a unique n-category satisfying these assumptions, and — if time permits — sketch how it looks in low dimensions.

This is based on work in progress with Theo Johnson-Freyd.

08:15 → 08:55 Steffens: On some of the mathematics of continuous symmetries

It is fair to say we have a rather complete mathematical framework for describing finite symmetries of field theories. I will discuss recent work on the mathematics of continuous symmetries. In particular, I will introduce a (in fact, several) higher category(ies) of `topological' (in the functional analytic sense) n-vector spaces together with, for each compact Lie group, a topological gauge theory (a BF theory) as a once-categorified fully extended theory with this target. Instead of invoking the cobordism hypothesis, I will write down a functor of n-categories explicitly; the construction may interpreted as a fully extended geometric quantization of the shifted cotangent of the group.

GCS '26 Paris.pdf

09:00 → 09:40 Müller: Fully local unitary topological quantum field theories

The action of generalized symmetries on an n-dimensional quantum field theory can be conveniently encoded by realizing it as a boundary of a topological field theory in one dimension higher, called the symmetry TQFT, using a sandwich construction. The extended operators of the symmetry TQFT give a concrete implementation of the categorical symmetry of the boundary. In fully local topological quantum field theories, there exists an operator–state correspondence, which identifies the possible extended operators with the higher categories of states that the TQFT assigns to manifolds of lower codimension. Taking unitarity into account in this setting requires the symmetry TQFT to be unitary and fully extended, which in turn calls for a not-yet-fully-developed theory of unitary higher categories. In my talk, I will explain some recent progress towards the definition and classification of unitary fully local topological quantum field theories. This is based on several joint works, involving (in part) Giovanni Ferrer, Brett Hungar, Theo Johnson-Freyd, Cameron Krulewski, Nivedita, David Penneys, David Reutter, Claudia Scheimbauer, Luuk Stehouwer, and Chetan Vuppulury, as well as ongoing work with Theo Johnson-Freyd, Cameron Krulewski, and Luuk Stehouwer.

talkLukas2 2.pdf

09:45 → 10:15 Coffee break

10:15 → 10:55 Parra-Martinez: Noether’s theorem, with a twist

Noether’s theorem, which relates continuous global symmetries and conserved currents, is perhaps one of the most famous results in theoretical physics. While it is well established for theories with a path integral formulation, its status for abstract QFTs is not settled. In this talk I will present a proof of Noether’s theorem following from the usual axioms of two-dimensional conformal field theory. In higher dimensions, I will argue that it is equivalent to the existence of twist defects for continuous global symmetries.

11:00 → 11:40 Heckman: TQFTs are in the Swampland

One of the recurring themes of recent years is the appearance of deep topological structures in the study of generalized global symmetries of quantum field theories. Perhaps surprisingly, then, there is also a general expectation that in quantum gravity, there are no global symmetries at all! In modern terminology, this is an example of a "Swampland Conjecture," namely that gravity imposes non-trivial constraints on the space of consistent low energy effective field theories. In this talk we give a brief overview of these expectations both from the top down and bottom up. We then present an argument showing that completely decoupled topological quantum field theory (TQFT) sectors are incompatible with basic features of holography. In particular, we argue that the fields of any TQFT necessarily couple to gravity both non-perturbatively and perturbatively in Newton's constant.

ParisSymmetries2026FINAL.pdf

lun. 29 juin

09:30 → 10:30 Yamashita: Towards categorical symmetry in TMF

I present duality results in equivariant TMF in my joint works with Ying-Hsuan Lin and David Gepner, which can be thought of as shadows of categorical symmetries in TMF. I discuss the ideas towards actually realizing fusion-category-equivariant TMF, joint work with Tomer Schlank.

10:30 → 11:00 Coffee

11:00 → 12:00 Utiralova: New examples of (non-semisimple) modular tensor categories

The talk is based on joint work with Victor Ostrik. I will describe a construction of braided finite tensor categories that generalizes the usual semisimplification construction applied to tilting modules over quantum groups. The categories we obtain are no longer semisimple, but (after an appropriate de-equivariantization procedure) modular. (At least) one of these categories gives a rather nice and small example of a category not Witt equivalent to a semisimple category, existence of which was not known before.

12:00 → 14:00 Lunch and private discussion

14:00 → 14:30 Czenky: Cochain valued TQFTs from nonsemisimple modular tensor categories

Consider a finite modular tensor category A. In [DGGPR] the authors exhibit a 3-dimensional topological field theory Z_A: Bord_A -> Vect, which, in the case where A is semisimple, recovers the usual Reshetikhin-Turaev TQFT. In the present work we show that this extends naturally to a TQFT which takes values in the symmetric tensor category of linear cochains. This cochain valued theory furthermore respects (certain classes of) homotopies.

[DGGPR] M. De Renzi, A. M. Gainutdinov, N. Geer, B. Patureau-Mirand, and I. Runkel. 3-dimensional TQFTs from non-semisimple modular categories. Sel. Math. New Ser., 28(2):42, 2022.

14:30 → 15:00 Hübner: On Frozen Singularities

Among the various corners of the string landscape frozen singularities belong to the less well-explored backgrounds. The central example of frozen ADE singularities, in M-theory, exhibit challenges reminiscent to those of RR-backgrounds in type II string theory. For these reasons much analysis in the literature has focussed on mappings to alternative duality frames where these challenges are recast in more tractable form. In this talk we aim to describe freezing directly in the fluxed backgrounds, and characterize frozen theories as confined phases of unfrozen theories.

15:00 → 15:30 Sanford: A primer on fusion categories over R

Fusion categories over R can be used to model time reversal symmetric (possibly composite) anyon systems. We will discuss several important aspects of the real setting that are different from what we have come to expect in the complex setting. Many examples will be given.

15:30 → 16:00 Open discussion about planning the week

18:15 → 20:15 Reception

mar. 30 juin

09:30 → 10:30 Stewart: String nets for twisted pivotal categories

14:00 → 15:00 Organized Discussion

Please add suggestions to https://docs.google.com/document/d/1C4teXxYc0RSsisdfJX9M1rgW8ulxnjtu1QueityBxJI/edit?usp=sharing

jeu. 2 juillet

09:30 → 10:30 Freed: Fully Local Reshetikhin-Turaev theories

11:00 → 12:00 Kapustin: Higher symmetries and lattice models

14:00 → 16:00 Informal discussion

Topics:
SO-invariance and central charges in 3D TQFT / 2D CFT
Classification of 4D TQFTs

ven. 3 juillet

09:30 → 10:30 Riva: An update on co-span constructions

11:00 → 12:00 Discussion: 4D TQFTs