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Fall 2023
$G$-structures on fusion categories have been shown to be an important tool to understand orbifolds of vertex operator algebras \cite{Kirillov}\cite{Gcrossedmuger}\cite{Orbifold_Paper}. We continue to develop this idea by generalizing Eilenberg-Maclane's notion of an Abelian $3$-cocycle to...
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Fall 2012
The main goal of this thesis is to explore various applications of persistent homology in statistical analysis of point-cloud data. In the introduction, after a brief historical overview, we provide some of the underlying concepts of persistence. Starting from Chapter 2 the focus is on analysis...
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Representations of affine truncations of representation involutive-semirings of Lie algebras and root systems of higher type
DownloadSpring 2011
An important component of a rational conformal field theory is a representation of a certain involutive-semiring. In the case of Wess-Zumino-Witten models, the involutive-semiring is an affine truncation of the representation involutive-semiring of a finite-dimensional semisimple Lie algebra. ...
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Spring 2019
Atkin and Swinnerton-Dyer conjectured a simple characterization of those Fuchsian groups whose modular forms have integral Fourier coefficient. It has a natural and far-reaching generalization, which we will call the vASD conjecture, to vector-valued modular forms. We confirm vASD conjecture for...