Lattice Methods, TQFTs, and Symmetries

Contribution List

1. Yamazaki - Topology in Lattice Yang–Mills Theory - 1

09/03/2026, 10:00

I will explore the role of nontrivial topological sectors in four-dimensional pure Yang–Mills theory. I will highlight lattice formulations and numerical Monte Carlo methods, and discuss new approaches for addressing the sign problem.

2. Kobayashi - ’t Hooft anomalies of exact/emergent symmetry on lattices - 1

09/03/2026, 11:00

I will talk about a way to characterize the ’t Hooft anomalies of exact/emergent symmetry on the lattices. The anomalies of exact invertible symmetry on lattices is characterized through Else-Nayak approach and its generalization, while those of emergent symmetry can be characterized through so-called generalized statistics. I will explain these two topics in sequential lectures.

3. Hsin - Automorphism is All You Need: Transversal Non-Clifford Gates in 2+1D and Higher Symmetries from Automorphism

09/03/2026, 12:00

We study automorphism in twisted gauge theories and discover they can give rise to generalized symmetries such as higher group and/or non-invertible symmetries. Using the automorphism symmetry, we discover transversal non-Clifford logical gates such as T gate in Clifford stabilizer models in 2+1D as well as CCZ gate in 5+1D self correcting non-Abelian quantum memory. The talk is based on...

4. Moroz - Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains - 1

09/03/2026, 15:00

Recent developments have revealed that symmetries need not form a group, but instead can be non-invertible. In these lectures I will use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a non-invertible symmetry is similar yet distinct from ordinary symmetry breaking. I will consider one-dimensional chains of group-valued qudits, whose local...

5. Runkel - From continuum to the lattice in conformal field theory - 1

09/03/2026, 16:00

When studying a 2d statistical system, one important question is to identify critical points and the corresponding universality class of critical behaviour, that is, the 2d conformal field theory which describes the statistical model at large length scales. In this talk, I
would like to discuss (but not answer) the converse question: starting from a 2d CFT, is there a way to construct lattice...

15. Yamazaki - Topology in Lattice Yang–Mills Theory - 2

10/03/2026, 10:00

I will explore the role of nontrivial topological sectors in four-dimensional pure Yang–Mills theory. I will highlight lattice formulations and numerical Monte Carlo methods, and discuss new approaches for addressing the sign problem.

32. Michele Fossati - TBA

10/03/2026, 11:00

16. Moroz - Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains - 2

10/03/2026, 12:00

Recent developments have revealed that symmetries need not form a group, but instead can be non-invertible. In these lectures I will use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a non-invertible symmetry is similar yet distinct from ordinary symmetry breaking. I will consider one-dimensional chains of group-valued qudits, whose local...

17. Kobayashi - ’t Hooft anomalies of exact/emergent symmetry on lattices - 2

10/03/2026, 15:00

I will talk about a way to characterize the ’t Hooft anomalies of exact/emergent symmetry on the lattices. The anomalies of exact invertible symmetry on lattices is characterized through Else-Nayak approach and its generalization, while those of emergent symmetry can be characterized through so-called generalized statistics. I will explain these two topics in sequential lectures.

18. Magdalena De La Fuente - Topological fault tolerance from a path-integral perspective - 1

10/03/2026, 16:00

Topological quantum error correction encodes quantum information in the ground space of a topologically ordered lattice system. To use such codes for reliable quantum computation, one must design low-overhead circuits that protect and manipulate the encoded information in a fault-tolerant way.

In these lectures, I focus on two-dimensional topological codes and fault-tolerant protocols...

19. Magdalena De La Fuente - Topological fault tolerance from a path-integral perspective - 2

11/03/2026, 10:00

Topological quantum error correction encodes quantum information in the ground space of a topologically ordered lattice system. To use such codes for reliable quantum computation, one must design low-overhead circuits that protect and manipulate the encoded information in a fault-tolerant way.

In these lectures, I focus on two-dimensional topological codes and fault-tolerant protocols...

20. Warman - Clifford-Hierarchy Gates from Group Quantum Doubles

11/03/2026, 11:00

A critical mission for realizing large-scale quantum computing is the development of simple and resource-efficient implementations of logical non-Clifford gates. This talk discusses how novel protocols for their implementation can be obtained from topological field theory.

In the first part, based on arXiv:2510.20890, we present hybrid lattice surgery between Abelian and non-Abelian codes...

21. Omori - Symmetry Spans and Enforced Gaplessness - 1

11/03/2026, 12:00

Anomaly matching for continuous symmetries has been the primary tool for establishing symmetry-enforced gaplessness. In this talk, I introduce a new mechanism based on symmetry spans: configurations in which a symmetry E is simultaneously embedded into two larger symmetries C and D. When the sets of gapped phases compatible with each embedding have no overlap, gaplessness is enforced.

In...

22. Gadde - TBA

11/03/2026, 15:00

23. Putrov - TBA

11/03/2026, 16:00

25. Honda - TBA - 1

12/03/2026, 10:00

24. Runkel - From continuum to the lattice in conformal field theory - 2

12/03/2026, 11:00

When studying a 2d statistical system, one important question is to identify critical points and the corresponding universality class of critical behaviour, that is, the 2d conformal field theory which describes the statistical model at large length scales. In this talk, I
would like to discuss (but not answer) the converse question: starting from a 2d CFT, is there a way to construct lattice...

26. Omori - Symmetry Spans and Enforced Gaplessness - 2

12/03/2026, 12:00

Anomaly matching for continuous symmetries has been the primary tool for establishing symmetry-enforced gaplessness. In this talk, I introduce a new mechanism based on symmetry spans: configurations in which a symmetry E is simultaneously embedded into two larger symmetries C and D. When the sets of gapped phases compatible with each embedding have no overlap, gaplessness is enforced.

In...

27. Delcamp - Dualities in quantum lattice models - 1

12/03/2026, 15:00

I will present a category theoretic framework to systematically study dualities between quantum lattice models. After discussing the interplay between twisted boundary conditions and charge sectors under such dualities, I will show how to construct isometries that relate the spectra of dual models. Along the way I will give practical tricks to apply the framework to your favourite...

28. Pflaum - C*-algebraic and topological study of quantum spin systems - 1

12/03/2026, 16:00

In the first lecture, the fundamentals of the C$^*$-algebraic approach to quantum many-body systems will be laid out. In particular, the topology and geometry of state spaces describing quantum lattice systems will be studied and a few old and new results on the state space of the quasi-local algebra of a quantum lattice spin system when endowed with either the natural metric topology or the...

29. Delcamp - Dualities in quantum lattice models - 2

13/03/2026, 10:00

I will present a category theoretic framework to systematically study dualities between quantum lattice models. After discussing the interplay between twisted boundary conditions and charge sectors under such dualities, I will show how to construct isometries that relate the spectra of dual models. Along the way I will give practical tricks to apply the framework to your favourite...

30. Pflaum - C*-algebraic and topological study of quantum spin systems - 2

13/03/2026, 11:00

In the first lecture, the fundamentals of the C$^*$-algebraic approach to quantum many-body systems will be laid out. In particular, the topology and geometry of state spaces describing quantum lattice systems will be studied and a few old and new results on the state space of the quasi-local algebra of a quantum lattice spin system when endowed with either the natural metric topology or the...

31. Honda - TBA - 2

13/03/2026, 12:00