nLab Theo Johnson-Freyd

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Selected writings

On extended TQFTs modelling topological phases of matter in solid state physics:

• Davide Gaiotto, Theo Johnson-Freyd, Condensations in higher categories (arXiv:1905.09566)

Construction of 2d SCFTs from error-correcting codes and suggestion that the Chern-Dold character from tmf to modular forms, sends a 2d SCFT to its partition function/elliptic genus/supersymmetric index:

• Davide Gaiotto, Theo Johnson-Freyd, Holomorphic SCFTs with small index, Canadian Journal of Mathematics , 74 2 (2022) 573-601 [arXiv:1811.00589, doi:10.4153/S0008414X2100002X]

and discussion of the 2d SCFTs (namely supersymmetric SU(2)-WZW-models) conjecturally corresponding, under this conjectural identification, to the elements of $\mathbb{Z}/24$ $\simeq$ $tmf^{-3}(\ast) = \pi_3(tmf)$ $\simeq$ $\pi_3(\mathbb{S})$ (the third stable homotopy group of spheres):

• Davide Gaiotto, Theo Johnson-Freyd, Edward Witten, p. 17 of: A Note On Some Minimally Supersymmetric Models In Two Dimensions, (arXiv:1902.10249) in S. Novikov et al. Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry, Proc. Symposia Pure Math., 103(2), 2021 (ISBN: 978-1-4704-5592-7)

• Davide Gaiotto, Theo Johnson-Freyd, Mock modularity and a secondary elliptic genus (arXiv:1904.05788)

• Theo Johnson-Freyd, Topological Mathieu Moonshine (arXiv:2006.02922)

On Lie groups and Lie algebras

• Mark Haiman (notes by Theo Johnson-Freyd), Lie groups, lecture notes, Berkeley (2008) [pdf]

and in the generality of quantum groups:

• Richard Borcherds, Mark Haiman, Theo Johnson-Freyd, Nicolai Reshetikhin, Vera Serganova: Berkeley Lectures on Lie Groups and Quantum Groups (2020-2024) [pdf]

On the relation between functorial quantum field theory (axiomatizing the Schrödinger picture of quantum field theory) and algebraic quantum field theory (axiomatizing the Heisenberg picture):

• Theo Johnson-Freyd, Heisenberg-picture quantum field theory, in Representation Theory, Mathematical Physics, and Integrable Systems, Progress in Mathematics 340 (2021) [arXiv:1508.05908, doi:10.1007/978-3-030-78148-4_13]

On higher dagger categories:

• Theo Johnson-Freyd, Dagger Higher Categories, workshop (2023) [web]

• Theo Johnson-Freyd, Higher Dagger Categories, talk at CQTS (08 Nov 2023) [slides:pdf, pdf, video:YT]

• Giovanni Ferrer, Brett Hungar, Theo Johnson-Freyd, Cameron Krulewski, Lukas Müller, Nivedita, David Penneys, David Reutter, Claudia Scheimbauer, Luuk Stehouwer, Chetan Vuppulury, Dagger n-categories [arXiv2403.01651]

On tmf in relation to elliptic genera as partition functions of 2d SCFTs:

• Theo Johnson-Freyd, Mayuko Yamashita, On the 576-fold periodicity of the spectrum SQFT: The proof of the lower bound via the Anderson duality pairing [arXiv:2404.06333]

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