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Welcome to the Pure Mathematics sub-community.

Research is organized into these collections:

• Pure Mathematics Department: Faculty, student, and staff research arranged by type. This collection does not include graduate Theses & Dissertations.
• Pure Mathematics Theses & Dissertations: Graduate student research required for degree completion.

### Recent Submissions

• #### On Asynchronous Interference Channels ﻿

(University of Waterloo, 2016-11-15)
In the first part of the thesis, a decentralized wireless network of separate transmitter-receiver pairs is studied where there is no central controller to assign the resources to the users and users do not explicitly ...
• #### The Enigma History and Mathematics ﻿

(University of Waterloo, 2016-10-25)
In this thesis we look at the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, ...
• #### COMPATIBILITY OF EXTENSIONS OF A COMBINATORIAL GEOMETRY ﻿

(University of Waterloo, 2016-09-29)
Two extensions of a geometry are compatible with each other if they have a common extension. If the given extensions are elementary, their compatibility can be intrinsically described in terms of their corresponding linear ...
• #### Classical Field Theory in the BV Formalism ﻿

(University of Waterloo, 2016-09-20)
This document is a review of the perspective on classical eld theories presented in [2] and [3].
• #### Strong Morita Equivalence and Imprimitivity Theorems ﻿

(University of Waterloo, 2016-09-15)
The purpose of this thesis is to give an exposition of two topics, mostly following the books \cite{R & W} and \cite{Wil}. First, we wish to investigate crossed product $C^*$-algebras in its most general form. Crossed ...
• #### Graph C*-algebras and the Abelian Core ﻿

(University of Waterloo, 2016-08-26)
We may associate to a C*-algebra to the directed graph E by associating edges to partial isometries and vertices to pairwise orthogonal Hilbert spaces which satisfy some additional conditions. Such graph algebras were first ...
• #### Some results on binary forms and counting rational points on algebraic varieties ﻿

(University of Waterloo, 2016-08-17)
In this thesis we study several problems related to the representation of integers by binary forms and counting rational points on algebraic varieties. In particular, we establish an asymptotic formula for $R_F(Z)$, the ...
• #### Nevanlinna-Pick Spaces and Dilations ﻿

(University of Waterloo, 2016-07-12)
The majority of this thesis is devoted to the study of Nevanlinna-Pick spaces and their multiplier algebras. These spaces are Hilbert function spaces in which a version of the Nevanlinna-Pick interpolation theorem from ...
• #### Exotic Group C*-algebras, Tensor Products, and Related Constructions ﻿

(University of Waterloo, 2016-06-15)
Recently there has been a rejuvenated interest in exotic group C*-algebras, i.e., group C*-algebras which are "intermediate" to the full and reduced group C*-algebras. This resurgence began with the introduction of the ...
• #### 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 ...
• #### Elliptic Curves over Finite Fields and their l-Torsion Galois Representations ﻿

(University of Waterloo, 2015-09-08)
• #### 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 ...

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