Browsing Pure & Applied Mathematics (Theses and Dissertations) by Title
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A dynamical study of the chirally rotated Schrödinger functional in lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)In this work, we present first results from dynamical simulations of the chirally rotated Schrödinger functional (SF) in lattice QCD. More specifically, we discuss the determination of renormalization constants of ... 
A formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetry
(Trinity College (Dublin, Ireland). School of Mathematics, 2008)In this thesis, we develop the Geometric Discretization formulation of DiracKahler fermions. We note that the naive definition of chiral synnnetry is only approximately captured in the formulation. However, we show that ... 
A theoretical study of spin filtering and its application to polarizing antiprotons
(Trinity College (Dublin, Ireland). School of Mathematics, 2008)There has been much recent research into possible methods of polarizing an antiproton beam, the most promising being spin filtering, the theoretical understanding of which is currently incomplete. The method of polarization ... 
The Ads/CFT spectrum via Integrabilitybased algorithms
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2017)The spectral problem of the AdS/CFT correspondence is believed to be integrable in the planar limit. The Quantum Spectral Curve captures the underlying mathematical structure in a relatively simple RiemannHilbert problem. ... 
Anisotropic discretisations and practical alltoall propagators for lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)In this thesis, we concern ourselves primarily with improving the accuracy of the determination of correlation functions in lattice QCD. We detail two avenues of improvement and implement them both, separately and in ... 
Aspects of ChernSimons theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2000)This thesis is based on 4 papers resulting from my work during my stay in the School of Mathematics, Trinity College Dublin. Each of them forms an individual part of the thesis. The relation between these parts is ... 
Aspects of the mathematical theory of water waves
(Trinity College (Dublin, Ireland). School of Mathematics, 2007)In this thesis we study various aspects of the mathematical theory of water waves. In Chapter 2 some qualitative results for two recentlyderived nonlinear models for shallow water waves are presented. In the first part ... 
The associative filtration of the dendriform operad
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)The associative filtration of the dendriform operad Norah Mohammed Alghamdi A dendriform algebra is a vector space V with two binary operations denoted < and > that satisfy the following three algebraic properties for all ... 
Black holes and string theory : selected topics
(Trinity College (Dublin, Ireland). School of Mathematics, 2001)This thesis is divided into three parts. In Part I the concept of holography in the context of the Maldacena conjecture and the threedimensional black hole of Banados, Teitelboim and Zanelli (BTZ) is studied. In particular, ... 
CFTs on Riemann surfaces of genus g ≥ 1
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)The purpose of this thesis is to argue that Npoint functions of holomorphic fields in rational conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulae for the 2point ... 
Charmed tetraquarks from lattice QCD
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018) 
Comparing the excitations of the periodic flux tube with effective string models.
(Trinity College (Dublin, Ireland). School of Mathematics, 2005)The spectrum of a periodic flux tube in pure SU(3) YangMills theory is evaluated nonperturbatively through computations on the lattice in the region from intermediate to long distances (1.5 < L < 4 fm ). For these flux ... 
Complexity of Holographic Flavours and causality in QFTs with GaussBonnet dual
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)This thesis is the compilation of two different projects undertaken during my PhD programme. Chapter 2 covers the work on quantum complexity. Quantum complexity of a thermofield double state in a strongly coupled quantum ... 
CR Singularities in condimension 2
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)In this thesis we study the real submanifolds of codimension 2 in a complex manifold near a CR singularity. The thesis has 3 chapters. In Chapter 1 we shall make a small introduction where we will remind some basic notions ... 
Cₒ(X)structure in C*algebras, multiplier algebras and tensor products
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)We begin in Chapter 2 with an introduction to the various notions of a bundle of C*algebras that have appeared throughout the literature, and clarify the definitions of upper and lowersemicontinuous C*bundles not ... 
Discrete exterior calculus with applications to flows and spinors
(Trinity College (Dublin, Ireland). School of Mathematics, 2005) 
Elements of an operator calculus
(Trinity College (Dublin, Ireland). School of Mathematics, 2001)The operational calculus developed by the Irish School of the Vienna Development Method (VDM) has a life of its own independent of its applications. This thesis is interested in the operational calculus that arose from the ... 
Extending geometric discretisation
(Trinity College (Dublin, Ireland). School of Mathematics, 2002)Geometric discretisation (GD) [1] is a novel approach capable of capturing topological properties, based on a correspondence between discrete objects and operations on a triangulation with continuum ones on a manifold. We ... 
Form Factors, Integrability and the AdS/CFT Correspondence
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018)Form factors are matrix elements of local operators between scattering states, and are interesting offshell objects in any QFT. In this thesis we will focus on the worldsheet theory describing strings in AdS5xS5, the ... 
Fourier analysis, multiresolution analysis and dilation equations
(Trinity College (Dublin, Ireland). School of Mathematics, 1998)This thesis has essentially two parts. The ﬁrst two chapters are an introduction to the related areas of Fourier analysis, multiresolution analysis and wavelets. Dilation equations arise in the context of multi resolution ...