School of Mathematics
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Pure & Applied Mathematics
Pure & Applied Mathematics
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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 stateoftheart spectroscopy ... 
YangBaxter integrable open quantum systems
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2023)The main result of this thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearestneighbour interaction and characterized by an Rmatrix of nondifference ... 
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 ... 
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. Finitevolume spectra are computed using distillation and the variational method. These spectra constrain ... 
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 fourdimensional N = 2 supersymmetric YangMills theory. By restricting the domain of the effective coupling to an appropriate fundamental domain the order parameter on the ... 
Modularity in Supersymmetric Gauge Theory
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)In this thesis, we study the modularity and duality of Coulomb branches for a class of fourdimensional N=2 supersymmetric gauge theories. For pure N=2 super YangMills theory with gauge group SU(2), the Coulomb branch can ... 
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 ... 
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 ... 
Characters, coadjoint orbits and DuistermaatHeckman integrals
(2021)The asymptotics of characters of irreducible representations of a compact Lie group G for large values of the scaling factor k are given by DuistermaatHeckman (DH) integrals over coadjoint orbits of G. This phenomenon ... 
Jordan systems, bounded symmetric domains and associated group orbits with holomorphic and CR extension theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)The first chapter will deal with the one to one correspondence between the positive hermitian Jordan triple systems and the bounded symmetric domains. We start by defining the various Jordan systems. Then we continue by ... 
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 ... 
A performance study of a template C++ class for parallel Monte Carlo simulations of local statistical field theories on a three dimensional lattice
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2020)In this thesis we investigate the performance properties of a template C++ class designed to run parallel Monte Carlo simulations of local statistical field theories on a three dimensional lattice. The generic nature of ... 
TT deformations of nonrelativistic models
(2021)The lightcone gauge approach to TT¯¯¯¯ deformed models is used to derive the TT¯¯¯¯ deformed matrix nonlinear Schrödinger equation, the LandauLifshitz equation, and the Gardner equation. Properties of onesoliton solutions ... 
Nonplanar anomalous dimensions in super YangMills theories
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)Conformal supersymmetric YangMills theories play an important role in the gaugegravity correspondence and, despite being highly nonphysical, have been a driving force for many new approaches in more realistic theories ... 
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 ... 
Integrable systems, separation of variables and the YangBaxter equation
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)This thesis is based on the author’s publications during the course of his PhD studies and focuses on various aspects of the field of quantum integrable systems. The aim of this thesis is to develop the socalled separation ... 
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 ... 
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' 
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 ... 
From positive geometries to a coaction on hypergeometric functions
(2020)It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on oneloop Feynman integrals in dimensional regularization, ...