Cobordism and Anomalies
This course builds the mathematical and physical foundations of cobordism theory and applies them to classify and compute anomalies in diverse quantum field theories and topological phases, culminating in discussions of recent research on discrete symmetry anomalies, fermionic TQFTs via symmetry extension, and symmetry-enforced gaplessness in 3+1 dimensions.
Lecturer
Date
8th April ~ 24th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-3-201 | ZOOM 06 | 537 192 5549 | BIMSA |
Syllabus
Lecture 1: Introduction to Cobordism Theory
Lecture 2: Bordism Spectra and Computations
Lecture 3: Invertible Field Theories and Cobordism Classification
Lecture 4: Anomaly Basics
Lecture 5: Cobordism Classification of Anomalies
Lecture 6: Examples — Anomalies in Gauge Theories
Lecture 7: Discrete Charge Anomalies and Bordism
Lecture 8: Discrete Anomalies in Physical Models
Lecture 9: Building Anomalous (3+1)d TQFTs
Lecture 10: Fermionic TQFTs via Symmetry Extension
Lecture 11: Symmetric Gapped States vs Symmetry-Enforced Gaplessness
Lecture 12: Advanced Topics and Research Frontiers
Lecture 2: Bordism Spectra and Computations
Lecture 3: Invertible Field Theories and Cobordism Classification
Lecture 4: Anomaly Basics
Lecture 5: Cobordism Classification of Anomalies
Lecture 6: Examples — Anomalies in Gauge Theories
Lecture 7: Discrete Charge Anomalies and Bordism
Lecture 8: Discrete Anomalies in Physical Models
Lecture 9: Building Anomalous (3+1)d TQFTs
Lecture 10: Fermionic TQFTs via Symmetry Extension
Lecture 11: Symmetric Gapped States vs Symmetry-Enforced Gaplessness
Lecture 12: Advanced Topics and Research Frontiers
Reference
1. Reflection positivity and invertible topological phases (Freed & Hopkins) arXiv: 1604.06527
2. Anomaly Inflow and the η-Invariant (Witten & Yonekura) arXiv: 1909.08775
3. Anomaly of 4d Weyl fermion with discrete symmetries (Zheyan Wan) arXiv: 2506.19710
4. Anomalous (3+1)d Fermionic Topological Quantum Field Theories via Symmetry Extension (Wan & Wang) arXiv: 2512.25038
5. How to Build Anomalous (3+1)d Topological Quantum Field Theories (Debray, Ye, Yu) arXiv: 2510.24834
6. Symmetric Gapped States and Symmetry-Enforced Gaplessness in 3-dimension (Debray, Ye, Yu) arXiv: 2602.12335
2. Anomaly Inflow and the η-Invariant (Witten & Yonekura) arXiv: 1909.08775
3. Anomaly of 4d Weyl fermion with discrete symmetries (Zheyan Wan) arXiv: 2506.19710
4. Anomalous (3+1)d Fermionic Topological Quantum Field Theories via Symmetry Extension (Wan & Wang) arXiv: 2512.25038
5. How to Build Anomalous (3+1)d Topological Quantum Field Theories (Debray, Ye, Yu) arXiv: 2510.24834
6. Symmetric Gapped States and Symmetry-Enforced Gaplessness in 3-dimension (Debray, Ye, Yu) arXiv: 2602.12335
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
I obtained my Bachelor's and Ph.D. degrees from the University of Science and Technology of China. Before my current position as an assistant professor at BIMSA, I was a postdoc at Yau Mathematical Sciences Center, Tsinghua University. My research interests lie in using topological methods (cobordism) to study theoretical physics (anomaly).