Browsing Pure Mathematics by Title
Now showing items 159-165 of 165
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Upper Bounds for the Number of Integral Points on Quadratic Curves and Surfaces
(University of Waterloo, 2010-04-27)We are interested in investigating the number of integral points on quadrics. First, we consider non-degenerate plane conic curves defined over Z. In particular we look at two types of conic sections: hyperbolas with ... -
Use-Bounded Strong Reducibilities
(University of Waterloo, 2009-08-20)We study the degree structures of the strong reducibilities $(\leq_{ibT})$ and $(\leq_{cl})$, as well as $(\leq_{rK})$ and $(\leq_{wtt})$. We show that any noncomputable c.e. set is part of a uniformly c.e. copy of ... -
Vector Bundles on Non-Kähler Elliptic Surfaces
(University of Waterloo, 2023-04-20)This thesis studies two problems relating to moduli spaces of vector bundles on non-Kähler elliptic surfaces. The first project involves the holomorphic symplectic structure on smooth and compact moduli spaces of sheaves ... -
Von Neumann Algebras for Abstract Harmonic Analysis
(University of Waterloo, 2008-08-28)This thesis develops the theory of operator algebras from the perspective of abstract harmonic analysis, and in particular, the theory of von Neumann algebras. Results from operator algebras are applied to the study of ... -
Weak Moment Maps in Multisymplectic Geometry
(University of Waterloo, 2018-07-04)We introduce the notion of a weak (homotopy) moment map associated to a Lie group action on a multisymplectic manifold. We show that the existence/uniqueness theory governing these maps is a direct generalization from ... -
The Weil conjectures
(University of Waterloo, 2008-01-24)In discussing the question of rational points on algebraic curves, we are usually concerned with ℚ. André Weil looked instead at curves over finite fields; assembling the counts into a function, he discovered that it ... -
Zigzags of Finite, Bounded Posets and Monotone Near-Unanimity Functions and Jónsson Operations
(University of Waterloo, 2009-09-25)We define the notion of monotone operations admitted by partially ordered sets, specifically monotone near-unanimity functions and Jónsson operations. We then prove a result of McKenzie's in [8] which states that if a ...