## Search

Now showing items 1-10 of 22

#### Families of Thue Inequalities with Transitive Automorphisms

(University of Waterloo, 2014-06-17)

A family of parameterized Thue equations is defined as F_{t,s,...}(X, Y ) = m, m ∈ Z
where F_{t,s,...}(X,Y) is a form in X and Y with degree greater than or equal to 3 and integer coefficients that are parameterized by ...

#### Semistable rank 2 co-Higgs bundles over Hirzebruch surfaces

(University of Waterloo, 2015-08-07)

It has been observed by S. Rayan that the complex projective surfaces that potentially
admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end
of the Enriques-Kodaira classification. ...

#### Digraph Algebras over Discrete Pre-ordered Groups

(University of Waterloo, 2013-01-25)

This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital ...

#### Some additive results in F_q[t]

(University of Waterloo, 2015-08-27)

We collected several results in integers of additive number theory and translated to results in F_q[t]. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, a ...

#### Some aspects of Cantor sets

(University of Waterloo, 2014-03-28)

For every positive, decreasing, summable sequence $a=(a_i)$, we can construct a Cantor set $C_a$ associated with $a$. These Cantor sets are not necessarily self-similar. Their dimensional properties and measures have been ...

#### Representations of Operator Algebras

(University of Waterloo, 2012-05-11)

The following thesis is divided into two main chapters. In Chapter 2 we study isometric representations of product systems of correspondences over the semigroup 𝐍ᵏ which are minimal dilations of finite dimensional, fully ...

#### Maximal ideal space techniques in non-selfadjoint operator algebras

(University of Waterloo, 2013-04-26)

The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the ...

#### Complexity of Classes of Structures

(University of Waterloo, 2013-08-28)

The main theme of this thesis is studying classes of structures with respect to various measurements of complexity. We will briefly discuss the notion of computable dimension, while the breadth of the paper will focus on ...

#### Generalized Complex Structures on Kodaira Surfaces

(University of Waterloo, 2014-08-05)

In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized ...

#### On the local positivity of line bundles on algebraic surfaces

(University of Waterloo, 2015-01-09)

In this thesis, we define a measure for how `positive' an effective line bundle is at a point on a variety, and prove that it is linear on the numerically effective subcone on a smooth, complete, toric surface.