## Search

Now showing items 11-20 of 66

#### 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.

#### The Mordell-Lang Theorem from the Zilber Dichotomy

(University of Waterloo, 2010-04-30)

We present a largely self-contained exposition of Ehud Hrushovski's proof of the function field Mordell-Lang conjecture beginning from the Zilber Dichotomy for differentially closed fields and separably closed fields. Our ...

#### The Eberlein Compactification of Locally Compact Groups

(University of Waterloo, 2013-01-24)

A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection ...

#### 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 ...

#### The Differential Geometry of Instantons

(University of Waterloo, 2009-08-07)

The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge ...

#### Interpolation Sets For Compact Abelian Groups

(University of Waterloo, 2014-09-04)

We will study various properties of I_0 and \epsilon-Kronecker sets.
We show that most infinite sets in the discrete dual group contain infinite interpolation sets.

#### Integral Moments of Quadratic Dirichlet L-functions: A Computational Perspective

(University of Waterloo, 2010-04-27)

In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have ...

#### Mean Curvature Flow in Euclidean spaces, Lagrangian Mean Curvature Flow, and Conormal Bundles

(University of Waterloo, 2011-08-10)

I will present the mean curvature flow in Euclidean spaces and the Lagrangian mean curvature flow. We will first study the mean curvature evolution of submanifolds in Euclidean spaces, with an emphasis on the case of ...

#### 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 ...

#### The Prouhet-Tarry-Escott problem

(University of Waterloo, 2013-01-15)

Given natural numbers n and k, with n>k, the
Prouhet-Tarry-Escott (PTE) problem asks for distinct
subsets of Z, say X={x_1,...,x_n} and
Y={y_1,...,y_n}, such that
x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. ...