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Now showing items 1-6 of 6

#### 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.

#### K-theory for C*-Algebras and for Topological Spaces

(University of Waterloo, 2015-04-27)

K-theory is the study of a collection of abelian groups that are invariant to C*-algebras or to locally compact Hausdorff spaces. These groups are useful for distinguishing C*-algebras and topological spaces, and they are ...

#### The Algebraic Kirchberg--Phillips Conjecture for Leavitt Path Algebras

(University of Waterloo, 2015-09-18)

This essay is meant to be an exposition of the theory of Leavitt path algebras and graph C*-algebras, with an aim to discuss some current classification questions. These two classes of algebras sit on opposite sides of a ...

#### 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. ...

#### 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 ...

#### Elliptic Curves over Finite Fields and their l-Torsion Galois Representations

(University of Waterloo, 2015-09-08)

Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ...