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Fall 2019

Xiaotian, Chang

We study the automorphism group of a non-singular hypersurface. We show that the automorphism group is finite in some conditions.

Fall 2019

Campbell, John

In the Journal of Algebra 323(2010) R. Barrington Leigh et al. derive the characters of the group of invertible 2 x 2 matrices over the integers modulo a power of an odd prime. We will generalize to certain local rings, and take quadratic extensions of this ring , by adjoining the root of a...

Spring 2019

Taylor, Mitchell A.

Suppose $X$ is a vector lattice and there is a notion of convergence $x{\alpha} \xrightarrow{\sigma} x$ in $X$. Then we can speak of an ``unbounded" version of this convergence by saying that $x{\alpha} \xrightarrow{u\sigma} x$ if $\lvert x\alpha-x\rvert \wedge u\xrightarrow{\sigma} 0$ for every...

Fall 2019

Wendlandt, Curtis

In the first part of this dissertation, we prove a generalization of a theorem of Drinfeld’s which allows one to rebuild the Yangian of an arbitrary simple Lie algebra starting from any of its finite-dimensional modules satisfying a non-triviality condition. This is achieved using the so-called...

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

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...

Spring 2019

Jenan Shtayat

Our main interest has to do with a conjecture of Nori, based on the weak Lefschetz theorem for Betti cohomology.We first prove Nori's conjecture under the assumption of the existence of a Bloch-Beilinson filtration.In the second part of my thesis, I re-prove a result of Paranjape on smooth...

Fall 2019

Ewanchuk, Logan

Recently, a new accounting standard was established, namely the International Financial Reporting Standard 9, requiring banks to build provisions using forward-looking expected loss models. When there is a significant increase in credit risk of a loan, additional provisions must be charged to the...

Fall 2019

Reimer, Jody Renae

Climate change is causing the Arctic to warm faster than anywhere else on earth. The projected effects of a warmer Arctic include changes in population dynamics and distributions, biodiversity, food web structure, and ecosystem services. Our ability to successfully monitor ecological changes and...

Fall 2019

Paul, Sounak

Classical methods of inference are often rendered inapplicable while dealing with data exhibiting heavy tails, which gives rise to infinite variance and frequent extremes, and long memory, which induces inertia in the data. In this thesis, we develop the Marcinkiewicz Strong Law of Large Numbers...