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Now showing items 31-38 of 38

#### 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 ...

#### 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 ...

#### On the Representation Theory of Semisimple Lie Groups

(University of Waterloo, 2010-08-30)

This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all ...

#### 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 ...

#### Asymptotic Distributions for Block Statistics on Non-crossing Partitions

(University of Waterloo, 2014-01-23)

The set of non-crossing partitions was first studied by Kreweras in 1972 and was known to play an important role in combinatorics, geometric group theory, and free probability. In particular, it has a natural embedding ...

#### Settling Time Reducibility Orderings

(University of Waterloo, 2010-04-28)

It is known that orderings can be formed with settling time domination and strong settling time domination as relations on c.e. sets. However, it has been shown that no such ordering can be formed when considering computation ...

#### 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. ...

#### 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 ...