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  • A dynamical study of the chirally rotated Schrödinger functional in lattice QCD 

    Brida, Mattia Dalla (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 

    Watterson, Steven (Trinity College (Dublin, Ireland). School of Mathematics, 2008)
    In this thesis, we develop the Geometric Discretization formulation of Dirac-Kahler fermions. We note that the naive definition of chiral synnnetry is only approximately captured in the formulation. However, we show that ...
  • A theoretical study of spin filtering and its application to polarizing antiprotons 

    O'Brien, Domhnaill (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 ...
  • Anisotropic discretisations and practical all-to-all propagators for lattice QCD 

    Ó Cais, Ailein (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 Chern-Simons theory 

    Prodanov, Emil Mihaylov (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 

    Henry, David (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 recently-derived nonlinear models for shallow water waves are presented. In the first part ...
  • Black holes and string theory : selected topics 

    Kennedy, Conall (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 three-dimensional black hole of Banados, Teitelboim and Zanelli (BTZ) is studied. In particular, ...
  • CFTs on Riemann surfaces of genus g ≥ 1 

    Leitner, Marianne (Trinity College (Dublin, Ireland). School of Mathematics, 2014)
    The purpose of this thesis is to argue that N-point functions of holomorphic fields in rational conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulae for the 2-point ...
  • Comparing the excitations of the periodic flux tube with effective string models. 

    Maresca, Francesca (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 ...
  • CR Singularities in condimension 2 

    Burcea, Valentin Daniel (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 

    McConnell, David (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 ...
  • Discrete exterior calculus with applications to flows and spinors 

    De Beaucé, Vivien (Trinity College (Dublin, Ireland). School of Mathematics, 2005)
  • Elements of an operator calculus 

    Hughes, Arthur (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 

    Sen, Samik (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 ...
  • Free Field Representation and Form Factors of the Chiral Gross-Neveu Model 

    Britton, Stephen (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 ...
  • Integrable lattice models for strongly correlated electrons 

    Quinn, Eoin (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 ...
  • Interferometry and non-equilibrium noise in the fractional quantum Hall effect 

    Smits, Olaf (Trinity College (Dublin, Ireland). School of Mathematics, 2014)
    We study theoretical aspects of fractional quantum Hall devices based on tunnelling point contacts. The fractional quantum Hall effect is the prime example of a (2 + 1) dimensional system with non-trivial topological order. ...
  • Large scale parallel network simulation 

    Lawless, Eoin (Trinity College (Dublin, Ireland). School of Mathematics, 2004)
    Simulation is one of the primary tools used in studying computer networks. However the difficulties of simulating a network grow with its size. With the hardware resources currently available it is not feasible to simulate ...
  • Logarithmic asymptotics in Queueing Theory and Risk Theory 

    Duffy, Ken (Trinity College (Dublin, Ireland). School of Mathematics, 2000)
    This thesis addresses four distinct, but related, problems. All four involve large deviation theory. The first problem is to relate the logarithmic asymptotics of the single server queue length distribution to the long ...
  • Methods for calculating option prices with early-exercise features 

    Cooney, Michael (Trinity College (Dublin, Ireland). School of Mathematics, 2006)
    In this dissertation we deal with two distinct methods for pricing financial options with early-exercise features. First we use finite difference methods to calculate the prices, examining in particular two new schemes ...