Browsing Pure & Applied Mathematics (Theses and Dissertations) by Title
Now showing items 17-36 of 68
-
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) Yang-Mills theory is evaluated non-perturbatively 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 Gauss-Bonnet 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 Anti-de Sitter spacetimes. In particular, we consider correlation functions with ... -
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 lower-semicontinuous 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, side-stepping the Maiani-Testa Theorem. This result is explored in ... -
Discrete exterior calculus with applications to flows and spinors
(Trinity College (Dublin, Ireland). School of Mathematics, 2005) -
Duality and domains in supersymmetric gauge theories
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)This thesis investigates duality properties of four-dimensional N = 2 supersymmetric Yang-Mills theory. By restricting the domain of the effective coupling to an appropriate fundamental domain the order parameter on the ... -
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 ... -
Exploring efficient methods for precision QCD calculations on the lattice
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2023)We study a new technique for stochastic noise reduction in the calculation of propagators by implementing it in OpenQ*D for two ensembles with O(a) improved Wilson fermion ac- tion, with periodic boundary conditions and ... -
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 off-shell objects in any QFT. In this thesis we will focus on the world-sheet theory describing strings in AdS5xS5, the ... -
Free Field Representation and Form Factors of the Chiral Gross-Neveu 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 ... -
Hadron Scattering Amplitudes from Lattice QCD
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2023)In this thesis we compute hadron scattering amplitudes within the framework of lattice quantum chromodynamics. Finite-volume spectra are computed using distillation and the variational method. These spectra constrain ... -
Heavy Hadron Spectroscopy from Lattice QCD
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2024)In this thesis, heavy hadron spectroscopy was studied through the formalism of lattice quantum chromodynamics. A summary of relevant theory is provided, followed by an overview of the current state-of-the-art spectroscopy ... -
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 sub-sector 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 ...
