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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 2013

Zeng, Linghang

This thesis focuses on characterizing an optimal trading strategy for a large trader, who has to buy (or sell) a fixed large volume over a given time period. We propose a model in discrete time, based on VWAP (Volume Weighted Average Price). The objective is to minimize expected deviations...

Spring 2014

Sebestyen, Mark D.

Geometrical lattice equivalences are used to generate over 100 new quadratic identities involving classical modular forms, Jacobi theta functions, θ2, θ3, θ4, and the Dedekind eta function η. Generalizations are examined and a seemingly new observation on the nature of η is noted.

Fall 2010

Chan, Pak-Keung

In this thesis, we discuss two separate topics from the theory of harmonic analysis on locally compact groups. The first topic revolves around the topological centers of module actions induced by unitary representations while the second one deals with the set of topologically invariant means...

Fall 2010

Li, Yin

Exponential Random Graph Models (ERGMs) have been developed for fitting social network data on both static and dynamic levels. However, the lack of large sample asymptotic properties makes it inadequate in assessing the goodness-of-fit of these ERGMs. Simulation-based goodness-of-fit plots were...

2002

Roberts, Andrew.

Spring 2019

Horak, Bohdan

This thesis investigates the hedging of equity-linked life insurance contracts with default time. In such a case the market is no longer complete and as such we consider imperfect hedging technique called Quantile Hedging. This hedging technique maximizes the probability of a successful hedge...

Fall 2013

Guzman, Ivan E

A Gelfand theory for an arbitrary Banach algebra A is a pair (G;A), such that: A is a C-algebra and G : A ! A is an algebra homomorphism; G induces a bijection between the set of maximal modular left ideals of A and the set of maximal modular left ideals of A; and for every maximal modular left...

Spring 2010

Ondrus, Alexander A.

The purpose of this thesis is to give a classification of anisotropic algebraic groups over number fields of higher real rank. This will complete the classification of algebraic groups over number fields of higher real rank, which was begun by V. Chernousov, L. Lifschitz and D.W. Morris in their...

Fall 2013

Dawson, Andria E

The Earth’s forests are of great economic, ecological, and social importance, and sustaining them is paramount for mitigating climate change. To successfully sus- tain forests we must understand their internal demographic dynamics and their relationship to climate. In this thesis, I developed...