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Fall 2019

Ooms, Adrien

In the framework of topological recursion (TR), the quantum curve conjecture relates the initial spectral curve to a differential equation – the quantum curve – satisfied by the TR wave-function. Several admissibility conditions have been put forward to explain which input of spectral curve...

Fall 2019

Huang, Qianhong

This thesis focuses on the measure algebra M(S) of a locally compact semitopological semigroup S. In particular, we consider the analog of the group algebra L1(G) of a locally compact group G on S and the topological amenability of S. Among other results which shall be explained further in...

Fall 2019

Glazyrina, Anna

In this thesis, selected topics on valuation and hedging of financial and insurance contracts are studied. First of all, we study the most common in mathematical finance Black-Scholes market and provide an alternative derivation of the famous Black-Scholes formula from the binomial option pricing...

Spring 2019

Bishop, Andrew E.

Let $G$ be a linear algebraic group defined over a ground field $k$, and let $\mu$ be a $\Gal(k^\sep/k)$-module.A \tb{cohomological invariant} is a morphism $a:H^1(-,G)\to H^n(-,\mu)$ of two functors from the category of field extensions over $k$ to the category of setswhere $H^1(-,G)$ is the...

Fall 2019

Pietrosanu, Matthew

With accelerating technological advancements, functional data analysis is of ever-growing importance in statistics, engineering, and medicine as the collection, storage, and analysis of data becomes ingrained in every aspect of modern life beyond any one field of study. From continuous biometric...

Fall 2019

Mitra, Joshua

The problem of benchmarking in financial markets is an important one. It could be a mutual fund looking to meet its cash inflows and outflows or a brokerage that has been contracted a benchmark price. There is also often incentive to manipulate benchmark. We introduce a discrete-time market model...

Fall 2019

Mackall, Eoin

This thesis investigates the Chow ring, and neighboring functors, of a Severi-Brauer variety. The approach taken here heavily depends on the computation of lower K-groups of a Severi-Brauer variety.We construct a functor (for an arbitrary scheme essentially of finite type over a field) that is a...

Fall 2019

Marculis, Nathan

Integrodifference equations are a common tool used in ecology to model the spread of populations. In this thesis, I explore the neutral genetic patterns formed by range expansions and how dispersal-reproduction trade-offs impact the spread of populations. In Chapter 2, we investigate the inside...

Spring 2019

Bernstein, Tobias

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...

Fall 2019

Liu,Zhengjun

Prostate cancer is one of the most common cancers among men in the world (excluding non-melanoma skin cancers). According to the statistics from the Canadian Cancer Society, it is the third leading cause of death from cancer in men in Canada. In general, prostate cancer is treatable with 5-year...