A head-shot of me near the southern Oregon coast

Theo Johnson-Freyd

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, 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 mentor is Kevin Costello. Other collaborators include Alex Chirvasitu, Owen Gwilliam, and Claudia Scheimbauer.


Research papers

Published and accepted for publication

  1. 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.)

  2. (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.)

  3. Spin, statistics, orientations, unitarity. 2015. To appear in Algebraic & Geometric Topology. (abstract, arXiv: 1507.06297.)

  4. 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.)

  5. 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.)

  6. 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).)

  7. 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.)

  8. 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).

  9. 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).

  10. 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).

Submitted for Publication

Other Preprints

Other documents


The following draft textbook (or rather, a finished version of it) has been accepted for publication by World Scientific:

A draft of Part I: Lie Groups, as well as the first chapter ofof Part II: Quantum Groups, is available. (DRAFT. PDF, TeX (tar.gz).) Chapters 1–6 of the full volume are almost exactly the same as the edited notes from M. Haiman (2008), but there have been some formatting changes. Chapter 7 is based mostly on lectures 20–31 of Anton's notes from the 2006 Tag Team Lie Groups course (PDF). Chapter 8 is drawn from the 2010 lectures by V. Serganova (unedited notes). Chapter 9 is from the 2009 lectures by N. Reshetikhin (unedited notes). Ultimately Part II will consist of between five and six chapters, based on the lectures by N. Reshetikhin (2009) and V. Serganova (2010).

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.

Grant and job application materials

Linked below are application materials I produced in Fall of 2012 for my postdoc search (which was quite successful):

I have made these materials available in part because of the request made by Ben Webster, whose job application materials were very useful for me when I was applying to postdocs. If you are a PhD student applying to postdocs and using these materials as guidance, I ask that you please do to things: (1) post your materials online, thereby helping younger people; (2) try to read many different friends' materials, because I don't know what parts of my applications helped me and what parts hurt.

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.

If you are curious, you can read the syllabus for my PhD Candidacy Qualifying Exam (UC Berkeley, 11 June 2009).

Seminar presentations













At Northwestern

At Berkeley

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