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Quantum Groups

- N. Reshetikhin, T. Johnson-Freyd
- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions… Expand

Symmetry protected topological phases and generalized cohomology

- D. Gaiotto, T. Johnson-Freyd
- MathematicsJournal of High Energy Physics
- 21 December 2017

A bstractWe discuss the classification of SPT phases in condensed matter systems. We review Kitaev’s argument that SPT phases are classified by a generalized cohomology theory, valued in the spectrum… Expand

Supersymmetry and the Suzuki chain

- T. Johnson-Freyd
- Mathematics
- 29 August 2019

We classify $N{=}1$ SVOAs with no free fermions and with bosonic subalgebra a simply connected WZW algebra which is not of type $\mathrm{E}$. The latter restriction makes the classification… Expand

Condensations in higher categories

- D. Gaiotto, T. Johnson-Freyd
- Mathematics
- 23 May 2019

We present a higher-categorical generalization of the "Karoubi envelope" construction from ordinary category theory, and prove that, like the ordinary Karoubi envelope, our higher Karoubi envelope is… Expand

(Op)lax natural transformations, twisted quantum field theories, and “even higher” Morita categories

- T. Johnson-Freyd, Claudia I. Scheimbauer
- Mathematics
- 23 February 2015

The Fundamental Pro-groupoid of an Affine 2-scheme

- A. Chirvasitu, T. Johnson-Freyd
- MathematicsAppl. Categorical Struct.
- 16 May 2011

TLDR

The Moonshine Anomaly

- T. Johnson-Freyd
- MathematicsCommunications in Mathematical Physics
- 26 July 2017

The anomaly for the Monster group $${\mathbb{M}}$$M acting on its natural (aka moonshine) representation $${V^\natural}$$V♮ is a particular cohomology class $${\omega^\natural \in {\rm… Expand

Poisson AKSZ theories and their quantizations

- T. Johnson-Freyd
- Mathematics
- 22 July 2013

We generalize the AKSZ construction of topological field theo- ries to allow the target manifolds to have possibly-degenerate up-to-homotopy Poisson structures. Classical AKSZ theories, which exist… Expand

On the coordinate (in)dependence of the formal path integral

- T. Johnson-Freyd
- Physics
- 30 March 2010

When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber… Expand

Reflexivity and dualizability in categorified linear algebra

- Martin Brandenburg, A. Chirvasitu, T. Johnson-Freyd
- Mathematics
- 21 September 2014

The "linear dual" of a cocomplete linear category $\mathcal C$ is the category of all cocontinuous linear functors $\mathcal C \to \mathrm{Vect}$. We study the questions of when a cocomplete linear… Expand

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