Browsing Pure & Applied Mathematics (Theses and Dissertations) by Title
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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 thermalization in holographic CFTs
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)This thesis covers a number of topics in conformal field theories that are supposed to have gravity duals according to the AdS/CFT correspondence. We use the conformal bootstrap in the Regge and lightcone limits as the ... 
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 ... 
Decay widths from Euclidean quantum field theory a scalar model and applications to QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2009)Lüscher provided a method by which the Euclidean correlation function, used in lattice field theories, can be used to evaluate the scattering phase shift, sidestepping the MaianiTesta Theorem. This result is explored in ... 
Discrete exterior calculus with applications to flows and spinors
(Trinity College (Dublin, Ireland). School of Mathematics, 2005) 
Efficient coding of sensory stimuli
(Trinity College (Dublin, Ireland). School of Mathematics, 2011)An important goal of mathematical neuroscience is to understand the coding principles governing the behaviour of sensory systems under stimulation. Here, we investigate the theory of efficient coding in nenral sensory ... 
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 ... 
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 ... 
Homotopical and effective methods for associative algebras
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)This thesis contains four main chapters based on four different papers. In the third chapter, we solve the problem of computing the minimal model of an arbitrary associative monomial algebra. Our methods are combinatorial ... 
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 ...