# Theo Johnson-Freyd

Dalhousie University

Areas of research:

### Overview

2016-present: Perimeter Institute (Postdoc) 2013-2016: Northwestern University (NSF Postdoc / Boas Assistant Professor) 2007-2013: UC Berkeley (PhD student) 2003-2007: Stanford (Undergraduate) prehistory-2003: Eugene, OR

### 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

- 5 Year Senior Postdoctoral Researcher, Perimeter Institute for Theoretical Physics, 2018-2020
- Postdoctoral Researcher, Perimeter Institute for Theoretical Physics, 2016-2017
- Boas Assistant Professor and NSF postdoctoral fellow, Department of Mathematics, Northwestern University, 2013-2016

### Awards

- 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., & Reutter, D. (n.d.). Minimal nondegenerate extensions. Journal of the American Mathematical Society, 37(1), 81-150. doi:10.1090/jams/1023
- Gaiotto, D., & Johnson-Freyd, T. (n.d.). Mock modularity and a secondary elliptic genus. Journal of High Energy Physics, 2023(8). doi:10.1007/jhep08(2023)094
- 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). 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 Unknown Book (pp. 203-221). American Mathematical Society. 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 (pp. 371-409). Springer International Publishing. 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 (pp. 345-370). Springer International Publishing. doi:10.1007/978-3-030-78148-4_12
- Johnson-Freyd, T. (2020). (3+1)D topological orders with only a $\mathbb{Z}_2$-charged particle. arxiv:2011.11165v1
- Johnson-Freyd, T., & Treumann, D. (2020). H4(Co0; Z) = Z/24. International Mathematics Research Notices, 2020(21), 7873-7907. doi:10.1093/imrn/rny219
- Johnson-Freyd, T. (2020). Topological Mathieu Moonshine. arxiv:2006.02922v2
- Johnson-Freyd, T. (2020). Correction to: The Moonshine Anomaly. Communications in Mathematical Physics, 375(2), 1579. doi:10.1007/s00220-019-03636-9
- Johnson-Freyd, T., Borcherds, R., Haiman, M., Reshetikhin, N., & Serganova, V. (2020). Berkeley Lectures on Lie Groups and Quantum Groups. World Scientific.

### Seminars

- Deeper Kummer theory, Mathematical Physics, 2023/09/21, PIRSA:23090104
- 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
- TMF and SQFT: questions and conjectures, Generalized Cohomology and Physics, ICTP, 2021/11/04
- A menagerie of N=1 SVOAs, NAAP, Kavli IPMU, 2021/10/06
- Semisimple higher categories, Western Hemisphere Colloquium on Geometry and Physics, Online, 2021/07/26
- Operators and (higher) categories in quantum field theory, Seminar on Arithmetic Geometry and Quantum Field Theory, Korea Institute for Advanced Study, 2021/07/23
- Higher S-matrices, TQFT Club, Instituto Superior Técnico, 2021/06/18
- Minimal nondegenerate extensions, Fusion Friday, AIM, 2021/06/11
- Minimal nondegenerate extensions and an anomaly indicator, Quantum Matter in Mathematics and Physics, CMSA, Harvard, 2021/06/10
- Classification of topological orders, Quantum Mathematics: Quantum Matter and Quantum Information, 75+1 CMS Summer Meeting, Canadian Mathematical Society, 2021/06/09
- Higher S-matrices, Higher Structures & Field Theory Seminar, UniVie/Erlangen/Würzburg/TUM, 2021/05/20
- The classification of topological orders, Mathematics Department Colloquium, OSU, 2021/04/01
- Fusion n-category Q&A, Fusion categories and tensor networks, AIM, 2021/03/12
- Orbifolds, Moonshine Learning Seminar, IAS, 2021/03/04
- Higher Galois closures, Seminar on Arithmetic Geometry and Quantum Field Theory, University of Warwick, 2021/03/03
- Strongly-fusion 2-categories are grouplike, Representation Theory Seminar, UMass Amherst, 2021/03/01
- Welcome and Opening Remarks, Women at the Intersection of Mathematics and Theoretical Physics, 2021/02/22, PIRSA:21020026
- Classification of topological quantum field theories, CTP Seminar, QMUL, 2021/01/01
- Condensations and components, University Quantum Symmetries Lectures, NCSU, 2021/01/01