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Skip to Search Results 7Frei, Christoph (Mathematical and Statistical Sciences)
 7Kong, Linglong (Mathematical and Statistical Sciences)
 7Lewis, Mark (Mathematical and Statistical Sciences)
 6Han, Bin (Mathematical and Statistical Sciences)
 6Hillen, Thomas (Mathematical and Statistical Sciences)
 6Mizera, Ivan (Mathematical and Statistical Sciences)

Fall 2021
In the United States, investors of exchangetraded funds (ETFs) and mutual funds are required to pay tax on the capital gains that their funds have made throughout the year. However, ETFs are able to avoid making taxable capital gains by taking advantage of a legal loophole, subsequently...

Fall 2021
The theory of convergence structures delivers a promising foundation on which to study general notions of convergence. However, that theory has one striking feature that stands out against all others: it is described using the language of filters. This is contrary to how convergence is used in...

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...

Fall 2021
Risk can be decomposed along two dimensions: risk allocation and risk attribution. On the one hand, the total risk of a company can be allocated to its divisions, using that the company’s profit/loss is the sum of the divisions’ profits/losses. On the other hand, risk is attributed to risk...

Fall 2022
Let n ≥ 3 and B ⊂ ℝⁿ. The Illumination Conjecture states that the minimal number I(B) of directions/‘light sources’ that illuminate the boundary of a convex body B, which is not the affine image of a cube, is strictly less than 2ⁿ. The conjecture in most cases is widely open, and it has only been...

Fall 2022
From the mechanical processes that produce the convolutions in the human brain needed for complex thought, to the precise and controlled movements derived by intuitive calculations of body position in figure skating, mechanics plays a role in everything we do. In this thesis, we apply and examine...

Monge solutions and uniqueness in multimarginal optimal transport: costs associated to graphs and a general condition
DownloadFall 2022
This thesis is devoted to the proof of several results on the existence and uniqueness of Monge solutions to the multimarginal optimal transportation problem. These results are found in Chapters \ref{Chapter3}, \ref{Chapter4} and \ref{Chapter5}, and represent joint work with Brendan Pass. The...

Fall 2022
In this thesis we study some aspects of `Airy structures' first proposed in \cite{ks}, as an algebraic reformulation of the ChekhovEynardOrantin (CEO) topological recursion initiated in \cite{eo} and \cite{eo1} in order to study the large $N$ expansion of matrix models. Our primary goal is to...

Fall 2022
This thesis concerns dynamical systems subject to small noise perturbations. Our purpose is to obtain a deep understanding of how small noise perturbations influence the original unperturbed dynamical system, especially over long but finite time intervals. We consider two special systems, the...

Fall 2022
Numerical methods are one of the most important aspects in the computer modelling of physical phenomena governed by differential equations. In order to study these phenomena precisely and in a timely manner, we need to use robust and efficient numerical methods for solving the underlying...