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

lun. 15 juin

1 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 Coffee break

2 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 Lunch break

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

3 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

4 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 Coffee break

5 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 Lunch break

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

6 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

7 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 Coffee break

8 Schlank

12:30 Lunch break

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

9 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 Poster session + Coffee break

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

jeu. 18 juin

10 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 Coffee break

11 Schlank

12:30 Lunch break

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

12 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

13 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 Coffee break

14 Schlank

12:30 Lunch break

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

15 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

16 McGreevy

17 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.

10:30 Coffee break

18 Córdova

19 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.

12:30 Lunch break

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

20 Zhang

21 Leung

16:00 Poster session + wine and cheese

mar. 23 juin

22 Krulewski

23 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.

10:30 Coffee break

24 Copetti

25 Antinucci

12:30 Lunch break

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

26 Zhu

27 Decoppet

28 Debray

17:30 Conference Reception

mer. 24 juin

29 Calaque

30 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.

10:30 Coffee break

31 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.

32 Rayhaun

12:30 Free Afternoon

jeu. 25 juin

33 Ji

34 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.

10:30 Coffee break

35 Reutter

36 Nivedita

12:30 Lunch break

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

37 Pace

38 Schäfer Nameki

ven. 26 juin

39 Parra-Martinez

40 Heckman

10:30 Coffee break

41 Steffens

42 Müller