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Now showing items 29-48 of 60

  • Higher Spin Theories in Twistor Space 

    HÄHNEL, PHILIPP (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 

    Tamaroff, Pedro Nicolas (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 ...
  • 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 ...
  • Integrable systems, separation of variables and the Yang-Baxter equation 

    Ryan, Paul (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 so-called separation ...
  • 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 ...
  • Methods of ascent and descent in multivariable spectral theory 

    Kitson, Derek (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 

    KORPAS, GEORGIOS (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 four-manifolds without boundary. We focus on the Donaldson-Witten theory, that is the N = 2 topologically ...
  • Multidimensional second order generalised stochastic processes on locally compact Abelian groups 

    Keville, Bernard (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 ...
  • Non-planar anomalous dimensions in super Yang-Mills theories 

    Spiering, Anne (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)
    Conformal supersymmetric Yang--Mills theories play an important role in the gauge-gravity correspondence and, despite being highly non-physical, have been a driving force for many new approaches in more realistic theories ...
  • Novel methods for heavy-quark physics from lattice QCD 

    Foley, Justin (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 mass-dependent errors ...
  • On the Symanzik improvement of gradient flow observables 

    RUBEO, ARGIA (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 

    Mainar, Pol Vilascea (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 ...
  • Pion-pion scattering amplitudes and timelike pion form factor from Nf=2+1 Lattice QCD 

    Hörz, Ben (Trinity College (Dublin, Ireland). School of Mathematics, 2017)
    We study isovector pion-pion 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 

    Golden, Darach (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 

    McGurk, Brian (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 

    Pluta, Robert (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 

    MacMaghnusa, Darran (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 ...