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 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 ... 
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) 
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 ... 
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 ... 
Free Field Representation and Form Factors of the Chiral GrossNeveu Model
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral ... 
Higher Spin Theories in Twistor Space
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018)In this thesis we formulate an action principle for conformal higher spin theory on twistor space. For this theory, and for a unitary subsector that we identify, we construct an MHV amplitude expansion by considering ... 
Integrable lattice models for strongly correlated electrons
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)This thesis is dedicated to the study of a new family of integrable lattice models for strongly correlated electrons, namely the Hubbard Shastry models. The techniques of exactly solvable models, and in particular those ... 
Interferometry and nonequilibrium noise in the fractional quantum Hall effect
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)We study theoretical aspects of fractional quantum Hall devices based on tunnelling point contacts. The fractional quantum Hall effect is the prime example of a (2 + 1) dimensional system with nontrivial topological order. ... 
Methods for calculating option prices with earlyexercise features
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)In this dissertation we deal with two distinct methods for pricing financial options with earlyexercise features. First we use finite difference methods to calculate the prices, examining in particular two new schemes ...