Browsing Mathematics and Statistics, Department of by Title
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The Tate Conjectures for Product and Quotient Varieties
(20130924)This thesis extends Tate’s conjectures from the smooth case to quotient varieties. It shows that two of those conjectures hold for quotient varieties if they hold for smooth projective varieties. We also consider arbitrary ... 
Tilting objects in derived categories of equivariant sheaves
(20080905)We construct classical tilting objects in derived categories of equivariant sheaves on quasiprojective varieties, which give equivalences with derived categories of modules over algebras. Our applications include a ... 
Topics in Combinatorics and Random Matrix Theory
(20090927)Motivated by the longest increasing subsequence problem, we examine sundry topics at the interface of enumerative/algebraic combinatorics and random matrix theory. We begin with an expository account of the increasing ... 
Topics related to vector bundles on abelian varieties
(20130625)This thesis is comprised of three logically independent parts. As the title suggests, each part is related to vector bundles on abelian varieties. We first use BrillNoether theory to study the geometry of a general ... 
Towards F=ma in a general setting for Lagrangian mechanics
(1998)By using a suitably general definition of a force, one may geometrically cast the EulerLagrange equations in a ``force balance'' form. The key ingredient in such a construction is the EulerLagrange 2force which is a ... 
Transcendence of Various Infinite Series and Applications of Baker's Theorem
(20091113)We consider various infinite series and examine their arithmetic nature. Series of interest are of the form $$\sum_{n =0}^{\infty} \frac{f(n)A(n)}{B(n)}, \;\;\;\; \sum_{n \in \mathbb{Z}}\frac{f(n)A(n)}{B(n)}, \;\;\;\; ... 
The twovariable Artin conjecture and elliptic analogues
In 1927, Emil Artin conjectured that for any integer a other than 1 or squares, the set of primes p for which a is a primitive root modulo p has positive density in the set of all primes. This was proven subject to the ... 
Unstable Brake Orbits in Symmetric Hamiltonian Systems
(20130925)In this thesis we investigate the existence and stability of periodic solutions of Hamiltonian systems with a discrete symmetry. The global existence of periodic motions can be proven using the classical techniques of ... 
Variational principles for constrained systems: theory and experiment
(1994)In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical system with constraints. The resulting equations are compared. Results are also ... 
Variations of Li's criterion for an extension of the Selberg class
(20120809)In 1997, XianJin Li gave an equivalence to the classical Riemann hypothesis, now referred to as Li's criterion, in terms of the nonnegativity of a particular infinite sequence of real numbers. We formulate the analogue ... 
Variations on Artin's Primitive Root Conjecture
(20110811)Let $a \in \mathbb{Z}$ be a nonzero integer. Let $p$ be a prime such that $p \nmid a$. Define the index of $a$ modulo $p$, denoted $i_{a}(p)$, to be the integer $i_{a}(p) := [(\mathbb{Z}/p\mathbb{Z})^{\ast}:\langle a ... 
Why is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology
(20190312)Sterility virulence, or the reduction in host fecundity due to infection, occurs in many host–pathogen systems. Notably, sterility virulence is more common for sexually transmitted infections (STIs) than for directly ...