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 geometrical approach to spike train noise
(Trinity College (Dublin, Ireland). School of Mathematics, 2012)Mathematically, spike trains are elusive processes. They encode information, although how this information is contained in a spike train is still not clear. Samestimulus spike trains display structural similarities, yet ... 
A nonperturbative study of the renormalisation of action parameters in anisotropic lattice QCD with applications to finite temperature QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2009)The advantages of using anisotropic lattices, instead of the more usual isotropic lattices, in QCD simulations are well estabhshed. Anisotropic lattices can be used to increase signal resolution and allow computational ... 
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 ... 
Automorphic Symmetries, String integrable structures and Deformations
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on ... 
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, ... 
THE CATLIN MULTITYPE OF SUMS OF SQUARES DOMAINS
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)Given a sum of squares domain of finite D' 
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) 
Coherent states and classical radiative observables in the Smatrix formalism
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)In this thesis, we study classical radiative observables perturbatively in terms of onshell scattering amplitudes. In particular, we focus primarily on the twobody problem in gauge and gravitational theories by using an ... 
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 ... 
Computational and mathematical aspects of Feynman integrals
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)This thesis covers a number of different research projects which are all connected to the central topic of computing Feynman integrals efficiently through analytic methods. Improvements in our ability to evaluate Feynman ... 
Conformal Bootstrap and Black Holes in AdS/CFT
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)In this thesis, we explore applications of the conformal bootstrap to holographic CFTs that are dual to theories of gravity in asymptotically Antide Sitter spacetimes. In particular, we consider correlation functions with ...