Theo Johnson-Freyd

Theo Johnson-Freyd's picture
Phd: University of California at Berkeley 2013

Area of Research:
Phone: (519) 569-7600 x7614

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

Research Interests

I study applications of higher category theory and homotopy theory to the 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.

Positions Held

  • 2013 - 2016 Department of Mathematics, Northwestern University Boas Assistant Professor and NSF postdoctoral fellow

Recent Publications

  • Spin, statistics, orientations, unitarity. Algebraic & Geometric Topology 17 (2017) 917-956 DOI: 10.2140/agt.2017.17.917. arXiv: 1507.06297
  • (Op)lax natural transformations, twisted field theories, and the "even higher" Morita categories. With Claudia Scheimbauer. Advances in Mathematics, 307 (2017) 147-223. DOI: 10.1016/j.aim.2016.11.014. arXiv: 1502.06526.
  • The quaternions and Bott periodicity are quantum Hamiltonian reductions. Symmetry, Integrability and Geometry: Methods and Applications, 12 (2016), 116, 6 pages. DOI: 10.3842/SIGMA.2016.116. arXiv: 1603.06603.
  • Tree- versus graph-level quasilocal PoincarĂ© duality on S1. Journal of homotopy and related structures, June 2016, Volume 11, Issue 2, pp 333-374. arXiv: 1412.4664
  • Homological perturbation theory for nonperturbative integrals. Letters in Mathematical Physics, November 2015, Volume 105, Issue 11, pp 1605-1632. arXiv: 1206.5319
  • 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. arXiv: 1409.5934
  • 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. arXiv: 1307.5812
  • The fundamental pro-groupoid of an affine 2-scheme. With Alex Chirvasitu. Applied Categorical Structures, Vol 21, Issue 5 (2013), pp. 469-522. arXiv: 1105.3104
  • The formal path integral and quantum mechanics. Journal of Mathematical Physics, 51, pp 122--103 (2010). arXiv: 1004.4305
  • 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. arXiv: 1003.1156
  • Symmetry protected topological phases and generalized cohomology. With Davide Gaiotto. arXiv: 1712.07950.
  • H4(Co0;Z)=Z/24. With David Treumann. arXiv: 1707.07587
  • The Moonshine Anomaly. arXiv: 1707.08388
  • Exact triangles, Koszul duality, and coisotopic boundary conditions. arXiv: 1608.08598
  • Heisenberg-picture quantum field theory. arXiv: 1508.05908
  • 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. arXiv: 1202.1554


  • T-duality for finite groups. Representation Theory, Mathematical Physics and Integrable Systems, CIRM, Luminy, France.
  • The fourth cohomology of some sporadic groups. Geometry, Symmetry and Physics, Yale.
  • Moonshine anomalies. Algebra seminar, University at Buffalo
  • Infinitely-categorified commutative algebra. Recent developments in noncommutative algebra and related areas, University of Washington
  • Moonshine anomalies. QMAP seminar, UC Davis.
  • Higher algebraic closures and phases of matter. Northeastern University
  • Moonshine anomalies. UT Austin.
  • Higher categories, generalized cohomology, and condensed matter. Representation Theory and Mathematical Physics, UC Berkeley
  • 576 Fermions. Algebra Seminar, Emory
  • Bott periodicity from Hamiltonian reduction. Number Theory and Algebraic Geometry. Boston College.
  • Exceptional structures, fermions, anomalies, and Hamiltonian reduction. Research Seminar in Mathematics, Northeastern
  • The Moonshine Anomaly. Higher Structures Lisbon, Instituto Superior Tecnico.
  • The Moonshine Anomaly. Maximals Seminar, University of Edinburgh.
  • Orbifolds of conformal field theories and cohomology of sporadic groups. Representation Theory, Geometry, and Combinatorics Seminar, UC Berkeley.
  • Advanced integration by parts: the BV formalism. Geometric Structures Laboratory, Fields Institute.
  • Fermionic hamiltonian reduction and periodicity. Geometry and Physics Seminar, Boston University.
  • Ideals in derived algebra and boundary conditions in AKSZ-type field theories. Representation Theory, Geometry, and Combinatorics Seminar, UC Berkeley.
  • 576 fermions, the Conway group, and tmf. Institute for Theoretical Physics, Stanford.
  • Bott periodicity via quantum Hamiltonian reduction. Representation Theory, Geometry, and Combinatorics Seminar, UC Berkeley.
  • PIRSA:17050013, Welcome and Opening Remarks, 2017-05-08, Quantum Field Theory on Manifolds with Boundary and the BV Formalism
  • PIRSA:16090051, Moonshine, topological modular forms, and 576 fermions., 2016-09-22, Mathematical Physics
  • PIRSA:15100110, Spin--Statistics and Categorified Galois Groups, 2015-10-23, Condensed Matter Physics and Topological Field Theory