A head-shot of me near the southern Oregon coast

Theo Johnson-Freyd

Senior Postdoctoral Fellow in Mathematical Physics,
Perimeter Institute for Theoretical Physics

e-mail: theojf@pitp.ca

Brief bio

My primary research is in an area I would call "homotopical physics": a mathematical physicist, I focus on quantum field theory, topological field theory, phases of condensed matter, "moonshine" phenoma, perturbative quantization, category theory, representation theory, and algebraic topology. For more details, see my publications and seminar presentations. For fewer details, see my Curriculum Vitae (PDF), which contains a strict subset of the information on this webpage.

I received my PhD from UC Berkeley in 2013, under the supervision of Nicolai Reshetikhin. I was then an NSF postdoc and Boas Assistant Professor at Northwestern University, and then at the Perimeter Institute. My postdoc mentors are Kevin Costello and Davide Gaiotto. Other collaborators include Alex Chirvasitu, Owen Gwilliam, Claudia Scheimbauer, and David Treumann.


Research papers

Published and accepted for publication

  1. H4(Co0;Z)=Z/24. With David Treumann. 2018. To appear in International Mathematics Research Notices. (abstract, arXiv: 1707.07587.)

  2. How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism. With Owen Gwilliam. Topology and Quantum Theory in Interaction, proceedings from the NSF-CBMS Regional Conference in the Mathematical Sciences that took place in Bozeman, Montana in 2017. (abstract, PDF, arXiv: 1202.1554.)

  3. The Moonshine Anomaly. 2018. Accepted pending revisions to Communications in Mathematical Physics. (abstract, arXiv:1707.08388.)

  4. Spin, statistics, orientations, unitarity. Algebraic & Geometric Topology 17 (2017) 917–956. (abstract, arXiv: 1507.06297, DOI: 10.2140/agt.2017.17.917.)

  5. (Op)lax natural transformations, twisted field theories, and the "even higher" Morita categories. With Claudia Scheimbauer. Advances in Mathematics, 307 (2017) 147–223. (abstract, arXiv: 1502.06526, DOI: 10.1016/j.aim.2016.11.014.)

  6. The quaternions and Bott periodicity are quantum Hamiltonian reductions. Symmetry, Integrability and Geometry: Methods and Applications, 12 (2016), 116, 6 pages. (abstract, arXiv: 1603.06603, DOI: 10.3842/SIGMA.2016.116.)

  7. Tree- versus graph-level quasilocal Poincaré duality on S1. Journal of homotopy and related structures, June 2016, Volume 11, Issue 2, pp 333–374. (abstract, arXiv: 1412.4664, DOI: 10.1007/s40062-015-0110-2.)

  8. Homological perturbation theory for nonperturbative integrals. Letters in Mathematical Physics, November 2015, Volume 105, Issue 11, pp 1605–1632. (abstract, arXiv: 1206.5319, DOI: 10.1007/s11005-015-0791-9.)

  9. Reflexivity and dualizability in categorified linear algebra. With Martin Brandenburg and Alexandru Chirvasitu. Theory and Applications of Categories, Vol. 30, No. 23, 2015, pp. 808–835. (abstract, arXiv: 1409.5934, published version (open access).)

  10. Poisson AKSZ theories and their quantizations. In Proceedings of the conference String-Math 2013, volume 88 of Proceedings of Symposia in Pure Mathematics, pages 291–306, Providence, RI, 2014. Amer. Math. Soc. (abstract, PDF (published version), arXiv: 1307.5812, DOI: 10.1090/pspum/088.)

  11. The fundamental pro-groupoid of an affine 2-scheme. With Alex Chirvasitu. Applied Categorical Structures, Vol 21, Issue 5 (2013), pp. 469–522. (abstract, arXiv: 1105.3104, DOI: 10.1007/s10485-011-9275-y).

  12. The formal path integral and quantum mechanics. Journal of Mathematical Physics, 51, 122103 (2010). (abstract, published PDF, DOI:10.1063/1.3503472, arXiv: 1004.4305, equation and theorem numbering differs between preprint and published versions).

  13. Feynman-diagrammatic description of the asymptotics of the time evolution operator in quantum mechanics. Letters in Mathematical Physics, November 2010, Volume 94, Issue 2, pp 123–149. (abstract, arXiv: 1003.1156, available Open Access from Springer Link at DOI: 10.1007/s11005-010-0424-2).

Other Preprints

Other documents


The following draft textbook has been accepted for publication by World Scientific:

It is based on lecture notes available below.

LiveTeXed Notes

I occasionally "Live-TeX" notes from classes and lectures. As with any notes, mine are replete with omissions and errors, undoubtedly; typing does allow me to catch questions from the audience and jokes from the professors, so these are included as well. Needless to say, anything good about the notes, and in particular presentation of the mathematical material, is due to the professor of the class. Anything bad about them, and in particular every inaccuracy, is mine. Use them with care. Also, please e-mail me with corrections: typos are trivial to fix, and mathematical errors should not be allowed to propagate. I was inspired to start typing lecture notes after watching Anton Geraschenko do it, and appreciate his advice.

Please note that the TAR.GZ files include TeX sources and plenty of other detritus: auxiliary files, partly completed problem sets, etc. You are welcome to download them, but I make no promises that the files will load on your computer: that will depend on whether your TeX installation exactly matches mine.

Miscellaneous mathematics

Here are two ideosyncratic notes surveying various mathematics:

As many graduate students discover when taking their language exams, you don't need any training in French in order to read Mathematical French. (It helps that Mathematical English is more French-inflected than is Colloquial English.) As evidence, I have translated into English Deligne's article Catégories Tensorielles (French original).

One of my more satisfying activities is that I am a reviewer for MathReviews and zbMath. Of my reviews, two appeared in the September 2012 print addition: MR2742432 (2012i:55005): Stolz and Teichner, Supersymmetric field theories and generalized cohomology, 2011 and MR2752518 (2012i:81001): Baez and Lauda, A prehistory of n-categorical physics, 2011.

Conference and seminar presentations














At Northwestern

At Berkeley

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