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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 geometrical approach to spike train noise 

    Gillespie, James B. (Trinity College (Dublin, Ireland). School of Mathematics, 2012)
    Mathematically, spike trains are elusive processes. They encode information, although how this information is contained in a spike train is still not clear. Same-stimulus spike trains display structural similarities, yet ...
  • A non-perturbative study of the renormalisation of action parameters in anisotropic lattice QCD with applications to finite temperature QCD 

    Morrin, Richard (Trinity College (Dublin, Ireland). School of Mathematics, 2009)
    The advantages of using anisotropic lattices, instead of the more usual isotropic lattices, in QCD simulations are well estabhshed. Anisotropic lattices can be used to increase signal resolution and allow computational ...
  • 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 ...
  • The Ads/CFT spectrum via Integrability-based algorithms 

    MARBOE, CHRISTIAN (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2017)
    The spectral problem of the AdS/CFT correspondence is believed to be integrable in the planar limit. The Quantum Spectral Curve captures the underlying mathematical structure in a relatively simple Riemann-Hilbert problem. ...
  • 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 ...
  • The associative filtration of the dendriform operad 

    ALGHAMDI, NORAH MOHAMMED (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)
    The associative filtration of the dendriform operad Norah Mohammed Alghamdi A dendriform algebra is a vector space V with two binary operations denoted < and > that satisfy the following three algebraic properties for all ...
  • 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 ...
  • Charmed tetraquarks from lattice QCD 

    THORNTON, BARRY WILLIAM (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018)
  • 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 ...
  • Complexity of Holographic Flavours and causality in QFTs with Gauss-Bonnet dual 

    GARCIA ABAD, FRANCISCO JOSE (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 ...
  • 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 ...
  • Decay widths from Euclidean quantum field theory a scalar model and applications to QCD 

    Nolan, Andrew (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 

    De Beaucé, Vivien (Trinity College (Dublin, Ireland). School of Mathematics, 2005)
  • Efficient coding of sensory stimuli 

    Greene, Garrett (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 ...