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Fall 2024
Let Cat(oo,oo) denote the (oo,1)-category of (oo,oo)-categories with weakly inductive equivalences. The main objective of this thesis is to demonstrate that Cat(oo,oo) satisfies universal properties with respect to homotopy-coherent internalisation and enrichment. To achieve these universal...
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Fall 2016
Little is known about Vertex Operator Algebras (VOAs) which are neither semi-simple nor rational, and most of the work on such VOAs has been focused around specific examples such as the Singlet VOA. In this thesis, the relationship between subcategories of the module categories of the Singlet VOA...
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Fall 2018
This thesis is about the theory of vertex operator algebras and their representations. Its main results provide new examples of logarithmic C2-cofinite vertex operator algebras. These include closure of the characters under modular transformations with explicit determination of the modular...
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Fall 2022
We consider the category of modules over certain subalgebras of the unrolled restricted quantum group associated to any reductive Lie algebra and show some progress towards the proof of an equivalence of categories of this with the category of local representations of a simple current extension.