Theo Johnson-Freyd

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 Poincaré 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
• 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

Seminars

• 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