Browsing Pure & Applied Mathematics (Theses and Dissertations) by Title
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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 ... 
Methods of ascent and descent in multivariable spectral theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2009)In this dissertation the theory of ascent and descent for a linear operator acting on a vector space is extended to arbitrary sets of operators and applied to the study of joint spectra for finite commuting systems of bounded ... 
Modern aspects of topological gauge theories  Polynomial invariants and mock modular forms
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)In this dissertation we present new results in the field of topologically twisted gauge theories evaluated on compact fourmanifolds without boundary. We focus on the DonaldsonWitten theory, that is the N = 2 topologically ... 
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 ... 
Multidimensional second order generalised stochastic processes on locally compact Abelian groups
(Trinity College (Dublin, Ireland). School of Mathematics, 2004)This thesis is concerned with the harmonic analysis of multidimensional generalised stochastic processes on locally compact Abelian groups. A multidimensional generalised stochastic process is a continuous linear operator ... 
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 ... 
Novel methods for heavyquark physics from lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)The application of 3+1 anisotropic lattices to numerical simulations of hadrons containing heavy quarks is investigated. It is expected that using a fine temporal lattice spacing will suppress large massdependent errors ... 
On the Symanzik improvement of gradient flow observables
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)The gradient flow provides a new class of renormalised observables which can be measured with high precision in lattice simulations. This is relevant for many interesting applications. However, such applications are made ... 
Peturbative study of the Chirally Rotated Schrödinger Functionality in Lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)In this thesis we study the renormalisation and O(a) improvement of the Chirally Rotated Schrödinger Functional (xSF) in perturbation theory. The xSF was originally proposed in [1] as a way of rehabiliting the mechanism ... 
Pionpion scattering amplitudes and timelike pion form factor from Nf=2+1 Lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2017)We study isovector pionpion scattering and extract the electromagnetic pion form factor in the timelike region from Nf = 2 + 1 Lattice QCD ensembles at a single lattice spacing and two pion masses mπ = 200MeV and mπ = ... 
Quality improvement using Alexander moves
(Trinity College (Dublin, Ireland). School of Mathematics, 2003)The objects under consideration in this work are simplicial meshes. We are interested in the geometric shape of the constituent simplices. This interest is justified by the impact of simplicial shape on the error bounds ... 
Random sampling and large deviations
(Trinity College (Dublin, Ireland). School of Mathematics, 2001)In this thesis, we are concerned with the effect of randomly sampling a stochastic process. We consider two stochastic processes: the underlying process, {Xt}tεT and the observation process {Tn}nεN, a strictly increasing ... 
Ranges of bimodule projections and conditional expectations
(Trinity College (Dublin, Ireland). School of Mathematics, 2011)The algebraic theory of comer subrings introduced by Lam (as an abstraction of the properties of Peirce corners eRe of a ring R associated with an idempotent e E R) are investigated here in the context of Banach and ... 
Resonances and lattice field theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2012)In this thesis, we look at the extraction of resonance parameters in lattice field theory. In particular we detail two major methods of dealing with resonances and consider them in a perturbative and nonpertnrbative ... 
Robust layerresolving methods for various Prandtl problems
(Trinity College (Dublin, Ireland). School of Mathematics, 2005)In this thesis we deal with four Prandtl boundary layer problems for incompressible laminar flow. When the Reynolds and Prandtl numbers are large the solution of each problem has parabolic boundary layers. For each problem ... 
Sigma models of the AdS/CFT correspondence
(Trinity College (Dublin, Ireland). School of Mathematics, 2011)The thesis is dedieated to the investigation of the properties of particular twodimensional quantum field theories, i.e. sigmamodels with target space of the form AdS5 x S5γ and AdS4 x CP3. The main results of the thesis ... 
Simulated annealing of Skyrme model configurations
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)The Skyrme model is a topological field theory that has been shown to be a good low energy approximation to QCD. A particular quantum theoretical treatment of the model reduces the quantization to a finitedimensional ... 
Solutions to dilation equations
(Trinity College (Dublin, Ireland). School of Mathematics, 2001)This thesis aims to explore part of the wonderful world of dilation equations. Dilation equations have a convoluted history, having reared their heads in various mathematical ﬁelds. One of the early appearances was in the ... 
Spectral functions from lattice QCD at finite temperature
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)An investigation of the bottonionium spectrum above and below the QCD deconfinement crossover temperature, Tc, was performed using a nonrelativistic treatment of the heavy quark on anisotropic lattices with Nf = 2 + 1 ... 
Spectroscopy and scattering of mesons containing charm quarks from lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)We present excited spectra of mesons containing charmlight (D), charmstrange (Ds) and charmcharm (charmoninm) combinations. We perform these spectroscopic calculations on two volumes. 16(3) X 128 and 24(3) x 128, of ...