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Spring 2024
Most quantum computers are based on elements with many addressable states, yet restrict themselves to a two-level subset, a qubit. In principle, more states could be used in each element to form a d-dimensional qudit, increasing the Hilbert space dimension and thus the computational power of the...
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Floquet Defect Mode Resonance and its Applications in Nonlinear, Quantum and Active Topological Silicon Photonics
DownloadSpring 2024
Topological photonic insulators are photonic quantum metamaterials whose transmission bands and bandgaps are characterized by certain topological invariants, which remain unchanged in the presence of lattice disorders. This resistance to defects has been exploited to realize integrated photonic...
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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 2021
Topological Recursion began its life as a series of recursive equations aimed at solving constraints which occur in matrix models of Quantum Field Theory. After its inception, Topological Recursion was given a more abstract formulation in terms of Quantum Airy Structures and has since been of...