A head-shot of me near the southern Oregon coast

Theo Johnson-Freyd

Boas Assistant Professor and NSF Postdoctoral Fellow,
Department of Mathematics, Northwestern University

e-mail: theojf at math dot northwestern dot edu
Office: 312 Lunt Hall, Northwestern University, Evanston, IL, 60202
Office Hours: By Appointment.

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. A more detailed description of my current research interests may be found by reading my recent research statement for the 2015-16 hiring season. For even more details, see my publications and seminar presentations. Of course, if you want fewer details, perhaps you want my Curriculum Vitae (PDF) or perhaps the shorter version; they contain a strict subset of the information on this webpage.

I received my PhD from UC Berkeley in 2013, under the supervision of Nicolai Reshetikhin. As an NSF postdoc, my sponsoring scientist at Northwestern is Kevin Costello. Other collaborators include Alex Chirvasitu, Owen Gwilliam, and Claudia Scheimbauer.


Research papers


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

  2. 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.)

  3. 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.)

  4. 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).)

  5. 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.)

  6. 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).

  7. 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).

  8. 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


I have an unfinited draft of a textbook on Lie theory, based on lectures given at UC Berkeley in 2006–08:

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 V. Serganova (2010). The first chapter of Part II: Quantum Groups has now been incorporated. Ultimately Part II will consist of between five and six chapters, based on the lectures by N. Reshetikhin (2009) and V. Serganova (2010).

Class 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 various application materials. I produced the following materials in Fall of 2015 for the tenure-track search:

And here are the materials I produced in Fall of 2012 for my postdoc search (which was relatively 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 — indeed, look more widely than just the Secret Blogging Seminar crowd, as theirs are the applications I read before writing mine, and perhaps we've just been propagating the same mistakes.

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


My husband and I are avid cooks. For a while we collected recipes and discussions at Local Seasoning. We are on hiatus right now, but may start up again.

In a previous life, I was a kitchen manager at Columbae House at Stanford University. Around the same time, I was also a dancer, and I choreographed the Opening Committee performance for the 2007 Stanford Viennese Ball (video).

Special effects powered by jQuery. This page was last update on Saturday, 25-Jun-2016 13:26:28 CDT.