Folder: courses/generalized-symmetries-course/notes

Oct 04, 2026

Sem II Week 3 — Spontaneous Breaking of Higher-Form Symmetries: the Landau Paradigm Regained

Oct 04, 2026

Sem II Week 4 — Gauging: Backgrounds, Orbifolds and the Quantum Dual Symmetry

Oct 04, 2026

Sem II Week 8 — The Toric Code, Solved to the Bone

Oct 04, 2026

Sem II Week 9 — Long-Range Entanglement and Error Correction

Oct 04, 2026

Sem II Week 10 — The Zoo Beyond ℤ₂: Quantum Doubles, Modular Data, Chern–Simons

Oct 04, 2026

Sem II Week 15 — Write-Up Presentations and Panoramic Closing

Oct 04, 2026

Week 2 — The Lattice as a Cell Complex: Chains, Cochains, and Duality

Oct 04, 2026

Week 3 — The Villain Form and the Exact Duality of the XY Model

Oct 04, 2026

Week 5 — Wegner's ℤ₂ Gauge Theory: Phases Without a Local Order Parameter

Oct 04, 2026

Week 11 — Compact U(1) in 4d: Monopole Condensation and the Dual Superconductor

Oct 04, 2026

Week 12 — θ-Terms, the Witten Effect, and Oblique Responses

Oct 04, 2026

Week 14 — Fradkin–Shenker II: Order Parameters Beyond Landau

Oct 04, 2026

Week 15 — Consolidation: Everything Was Symmetry All Along

Oct 03, 2026

Sem II Week 11 — String-Net Condensation: Wen's Mechanism for Emergent Gauge Fields

Oct 03, 2026

Sem II Week 12 — Modified Villain: Exact Dualities and Exact Higher-Form Symmetries on the Lattice

Oct 03, 2026

Sem II Week 13 — Non-Invertible Symmetries: Duality Defects and Condensation Defects

Oct 02, 2026

Sem II Week 1 — Symmetries Are Topological Operators

Oct 02, 2026

Sem II Week 2 — ℤ_N Gauge Theory as BF Theory: the Universal Topological Skeleton

Oct 02, 2026

Sem II Week 5 — 't Hooft Anomalies: Obstruction as Physics

Oct 02, 2026

Sem II Week 6 — Mixed Higher-Form Anomalies: Yang–Mills at θ = π

Oct 02, 2026

Sem II Week 7 — SPT Phases, Group Cohomology, Dijkgraaf–Witten

Oct 02, 2026

Week 7 — Kogut–Susskind: the Hamiltonian Lattice

Oct 02, 2026

Week 8 — Midterm and Dual Variables for Abelian Gauge Theories

Sep 29, 2026

Week 4 — BKT, Kramers–Wannier, and the First Disorder Operators

Sep 29, 2026

Week 9 — Compact QED₃ I: the Monopole Plasma

Sep 29, 2026

Week 10 — Compact QED₃ II: the Mass Gap and the Area Law

Sep 29, 2026

Week 13 — Fradkin–Shenker I: Gauge–Higgs Systems

Sep 28, 2026

Week 1 — Compact Variables and Their Defects: the XY Model

Sep 28, 2026

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Folder: courses/generalized-symmetries-course/notes

Sem II Week 3 — Spontaneous Breaking of Higher-Form Symmetries: the Landau Paradigm Regained

Sem II Week 4 — Gauging: Backgrounds, Orbifolds and the Quantum Dual Symmetry

Sem II Week 8 — The Toric Code, Solved to the Bone

Sem II Week 9 — Long-Range Entanglement and Error Correction

Sem II Week 10 — The Zoo Beyond ℤ₂: Quantum Doubles, Modular Data, Chern–Simons

Sem II Week 15 — Write-Up Presentations and Panoramic Closing

Week 2 — The Lattice as a Cell Complex: Chains, Cochains, and Duality

Week 3 — The Villain Form and the Exact Duality of the XY Model

Week 5 — Wegner's ℤ₂ Gauge Theory: Phases Without a Local Order Parameter

Week 11 — Compact U(1) in 4d: Monopole Condensation and the Dual Superconductor

Week 12 — θ-Terms, the Witten Effect, and Oblique Responses

Week 14 — Fradkin–Shenker II: Order Parameters Beyond Landau

Week 15 — Consolidation: Everything Was Symmetry All Along

Sem II Week 11 — String-Net Condensation: Wen's Mechanism for Emergent Gauge Fields

Sem II Week 12 — Modified Villain: Exact Dualities and Exact Higher-Form Symmetries on the Lattice

Sem II Week 13 — Non-Invertible Symmetries: Duality Defects and Condensation Defects

Sem II Week 1 — Symmetries Are Topological Operators

Sem II Week 2 — ℤ_N Gauge Theory as BF Theory: the Universal Topological Skeleton

Sem II Week 5 — 't Hooft Anomalies: Obstruction as Physics

Sem II Week 6 — Mixed Higher-Form Anomalies: Yang–Mills at θ = π

Sem II Week 7 — SPT Phases, Group Cohomology, Dijkgraaf–Witten

Week 7 — Kogut–Susskind: the Hamiltonian Lattice

Week 8 — Midterm and Dual Variables for Abelian Gauge Theories

Week 4 — BKT, Kramers–Wannier, and the First Disorder Operators

Week 9 — Compact QED₃ I: the Monopole Plasma

Week 10 — Compact QED₃ II: the Mass Gap and the Area Law

Week 13 — Fradkin–Shenker I: Gauge–Higgs Systems

Week 1 — Compact Variables and Their Defects: the XY Model

Week 6 — Wilson's Formulation: Compact Groups, Haar Measure, Strong Coupling