# Theo Johnson-Freyd

Dalhousie University

Areas of research:

### Teaching Affiliations

If you are interested in pursuing a MSc degree, please apply to the Perimeter Scholars International (PSI) masters program. If you are interested in working with me as a PhD student, please send me an email at [email protected] or submit an application directly to my department at Dalhousie University and indicate that you would like to be supervised by me. Perimeter Institute is committed to diversity within its community and I welcome applications from underrepresented groups.

### Research Interests

I study applications of higher category theory and homotopy theory to quantum field theory and to condensed matter, and I study applications of condensed matter and quantum field theory to homotopy theory and higher category theory. My main focus right now is on "global categorical symmetry": the study of topological extended objects in quantum field theories. The mathematics of these objects is higher category theory, and specifically the theory of higher fusion categories and topological quantum field theory. (The name "fusion" comes from the fusion of point particles, and by extension larger-dimensional objects.) I also work on elliptic cohomology (aka topological modular forms) and sporadic objects (e.g. the Monster group and Moonshine). These two subjects, seemingly disjoint, in fact intersect, in particular in the world of 1+1D supersymmetric and superconformal field theories.

### Positions Held

- Associate Professor, Mathematics and Statistics, Dalhousie University, 2024-present
- Assistant Professor, Mathematics and Satistics, Dalhousie University, 2021-2024
- Associate Faculty, Perimeter Institute, 2021-present
- Senior Postdoctoral Researcher, Perimeter Institute, 2016-2020
- Boas Assistant Professor and NSF postdoctoral fellow, Department of Mathematics, Northwestern University, 2013-2016

### Awards

- President's Research Excellence Award for Emerging Investigators, Dalhousie University, 2024
- Simons Collaboration: "Global Categorical Symmetries", Simons Foundation, 2021-2026
- Discovery Grant "The Higher Algebra of Spaces of Quantum Systems", Natural Sciences and Engineering Research Council of Canada (NSERC), 2021-2026
- Accelerator Supplement: "The Higher Algebra of Spaces of Quantum Systems", Natural Sciences and Engineering Research Council of Canada (NSERC), 2021-2026
- Early Career Researcher top-up: "The Higher Algebra of Spaces of Quantum Systems", Natural Sciences and Engineering Research Council of Canada (NSERC), 2021-2026

### Recent Publications

- Johnson-Freyd, T., & Yamashita, M. (2024). On the 576-fold periodicity of the spectrum SQFT: The proof of the lower bound via the Anderson duality pairing.
- Ferrer, G., Hungar, B., Johnson-Freyd, T., Krulewski, C., Müller, L., Nivedita., . . . Vuppulury, C. (2024). Dagger $n$-categories. doi:10.48550/arxiv.2403.01651
- Gaiotto, D., & Johnson-Freyd, T. (n.d.). Mock modularity and a secondary elliptic genus. Journal of High Energy Physics, 2023(8), 94. doi:10.1007/jhep08(2023)094
- Johnson-Freyd, T., & Reutter, D. (n.d.). Minimal nondegenerate extensions. Journal of the American Mathematical Society, 37(1), 81-150. doi:10.1090/jams/1023
- Furet, A., & Johnson-Freyd, T. (2023). Ground-state degeneracy of twisted sectors of Conway Moonshine SCFT. arxiv:2305.05081v1
- Johnson-Freyd, T., & Yu, M. (n.d.). Topological Orders in (4+1)-Dimensions. SciPost Physics, 13(3), 068. doi:10.21468/scipostphys.13.3.068
- Johnson-Freyd, T. (2022). On the Classification of Topological Orders. Communications in Mathematical Physics, 393(2), 989-1033. doi:10.1007/s00220-022-04380-3
- Gaiotto, D., & Johnson-Freyd, T. (2022). Holomorphic SCFTs with small index. Canadian Journal of Mathematics, 74(2), 573-601. doi:10.4153/s0008414x2100002x
- JOHNSON-FREYD, T., & YU, M. (2021). FUSION 2-CATEGORIES WITH NO LINE OPERATORS ARE GROUPLIKE. Bulletin of the Australian Mathematical Society, 104(3), 434-442. doi:10.1017/s0004972721000095
- Gaiotto, D., Johnson-Freyd, T., & Witten, E. (2021). A Note On Some Minimally Supersymmetric Models In Two Dimensions. In Integrability, Quantization, and Geometry (Vol. 103.2, pp. 203-221). American Mathematical Society (AMS). doi:10.1090/pspum/103.2/01857
- Johnson-Freyd, T. (n.d.). Supersymmetry and the Suzuki chain. Tunisian Journal of Mathematics, 3(2), 309-359. doi:10.2140/tunis.2021.3.309
- Johnson-Freyd, T. (2021). Heisenberg-Picture Quantum Field Theory. In Representation Theory, Mathematical Physics, and Integrable Systems (Vol. 340, pp. 371-409). Springer Nature. doi:10.1007/978-3-030-78148-4_13
- Johnson-Freyd, T. (2021). Galois Action on VOA Gauge Anomalies. In Representation Theory, Mathematical Physics, and Integrable Systems (Vol. 340, pp. 345-370). Springer Nature. doi:10.1007/978-3-030-78148-4_12

### Seminars

- Quantum homotopy group, Categorical Symmetries in Quantum Field Theory, University of Edinburgh, Edinburgh, United Kingdom, 2024/06/17
- Quantum homotopy groups, Thematic Program in Field Theory and Topology, University of Notre Dame, South Bend, IN, United States, 2024/06/12
- The universal target category, Harvard University, Cambridge, United States, 2024/05/02
- The universal target category, Johns Hopkins University, Baltimore, United States, 2024/04/11
- Quantum homotopy groups, Higher Categorical Tools for Quantum Phases of Matter, 2024/03/21, PIRSA:24030091
- Higher Dagger Categories, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates, 2023/11/08
- Deeper Kummer theory, Mathematical Physics, 2023/09/21, PIRSA:23090104
- SVOAs and some exceptional groups, Universität Hamburg, Hamburg, Germany, 2023/08/22
- Super Duper Vector Spaces II: The higher-categorical Galois group of R, Higher Structures in Functorial Field Theory, University of Regensburg, Regensburg, Germany, 2023/08/18
- Topological Umbral Moonshine, Topological Moonshine, University of Illinois at Urbana-Champaign, Mathematics, Urbana, United States, 2023/07/17
- Higher algebraic closure, OWSM Seminar, University of Oxford, Mathematics Institute, Oxford, United Kingdom, 2023/05/19
- Higher algebraic closure, The Ohio State University, Mathematics, Columbus, United States, 2023/04/27, Video URL
- Higher algebraic closure, Higher Structures Seminar, Feza Gürsey Institute, Istanbul, Turkey, 2023/04/11
- Homotopy Quantum Groups, 2022 Simons Collaboration on Global Categorical Symmetries Annual Meeting, Simons Foundation, New York, United States, 2022/11/18, Video URL
- SVOAs and some exceptional groups, Quantum Symmetries, Centre de Recherches Mathématics, Montreal, Canada, 2022/10/25, Video URL
- A 4D TQFT which is not (quite) a gauge theory, Symmetry Seminar, University of Oxford, Mathematics Institute, Oxford, United Kingdom, 2022/10/04, Video URL
- Hypergroups and fusion higher categories, Higher categories and topological order, American Institute of Mathematics, Palo Alto, United States, 2022/09/29
- What is a fusion higher category?, Higher Symmetry and Quantum Field Theory, Aspen Center For Physics, Aspen, United States, 2022/09/09
- Welcome and Opening Remarks, Global Categorical Symmetries, 2022/06/13, PIRSA:22060023
- Welcome and Opening Remarks, Global Categorical Symmetries, 2022/06/06, PIRSA:22060006
- Classification of (semisimple) TQFTs, Math QFT seminar, MPIM, 2022/03/29
- Why the spaces of N=(0,1) susy QFTs form a spectrum?, Stolz-Teichner Seminar, Oxford, 2022/03/07
- Categorified algebraic closure, ATCAT, Dalhousie, 2022/02/15
- Algebraically closed higher categories, Geometry and Topology Seminar, Haifa, 2021/12/05
- Algebraically closed higher categories, Mathematical Physics, 2021/12/03, PIRSA:21120010