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Quantum Groups
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
Symmetry protected topological phases and generalized cohomology
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
Supersymmetry and the Suzuki chain
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
Condensations in higher categories
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
The Fundamental Pro-groupoid of an Affine 2-scheme
A new notion of “commutative 2-ring” that includes both Grothendieck topoi and symmetric monoidal categories of modules, and a notion of π1 for the corresponding “affine 2-schemes” helps to simplify and clarify some of the peculiarities of the étale fundamental group.
The Moonshine Anomaly
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
Poisson AKSZ theories and their quantizations
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
On the coordinate (in)dependence of the formal path integral
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
Reflexivity and dualizability in categorified linear algebra
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