School of Mathematics: Recent submissions

Now showing items 21-40 of 390

    • A family of compact strictly pseudoconvex hypersurfaces in C^2 without umbilical points 

      ZAITSEV, DMITRI; Ebenfelt, Peter; Ngoc Son, Duong (2018)
      We prove the following: For ϵ>0, let Dϵ be the bounded strictly pseudoconvex domain in ℂ2 given by (log|z|)2+(log|w|)2<ϵ2. The boundary Mϵ:=∂Dϵ⊂ℂ2 is a compact strictly pseudoconvex CR manifold without umbilical ...

    • Yang-Mills instantons on the taub-NUT space and supersymmetric N=2 gauge theories with impurities 

      O'Hara, Clare (Trinity College (Dublin, Ireland). School of Mathematics, 2010)
      We write a formula for arbitrary charge calorons, instantons on R3 x S1, in terms of the Green's function of the Laplacian defined for the Nahm Transform, thus generalising the formula for the charge one caloron derived ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • Sigma models of the AdS/CFT correspondence 

      Bykov, Dmitry Vladimirovich (Trinity College (Dublin, Ireland). School of Mathematics, 2011)
      The thesis is dedieated to the investigation of the properties of particular two-dimensional quantum field theories, i.e. sigma-models with target space of the form AdS5 x S5γ and AdS4 x CP3. The main results of the thesis ...

    • QCD Coupling from a Nonperturbative Determination of the Three-Flavor ?? Parameter 

      Sint, Stefan; Fritzsch, Patrick (2017)
      We present a lattice determination of the Λ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from 0.2 to 70 GeV, and using ...

    • High precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks 

      Sint, Stefan (SpringerOpen, 2019)
      We determine the non-perturbatively renormalized axial current for O(a) improved lattice QCD with Wilson quarks. Our strategy is based on the chirally rotated Schrödinger functional and can be generalized to other finite ...

    • 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 ...

    • An Anisotropic preconditioning for the Wilson fermion matrix on the lattice 

      Peardon, Michael (2010)
      A preconditioning for the Wilson fermion matrix on the lattice is defined, which is particularly suited to the case when the temporal lattice spacing is much smaller than the spatial one. Details on the implementation of ...

    • Phase shift with LapH propagators 

      Peardon, Michael (2010)
      The pion-pion scattering phase shift is computed using LapH propagators. The LapH method for computing quark propagators is used to form two-particle correlation functions with a number of different operators. Excited ...

    • A novel method for evaluating correlation functions in lattice hadron spectroscopy 

      Peardon, Michael (2010)
      We describe a new approach for evaluating hadronic correlation functions which combines Laplacian-Heaviside quark smearing with a stochastic estimator of quark propagators. This method utilizes noise ...

    • The excited hadron spectrum in lattice QCD using a new variance reduction method 

      Peardon, Michael (2010)
      Progress in calculating the spectrum of excited baryons and mesons in lattice QCD is described. Correlation matrices of sets of spatially-extended hadron operators have been studied and their effectiveness in facilitating ...

    • String breaking with 2+1 dynamical fermions using the stochastic LapH-method 

      Peardon, Michael (2018)
      The static potential V(r) between a static quark and a static antiquark separated by a distance r is defined as the energy of the ground state of the system. As a consequence of confinement, the energy between the ...

    • String breaking by light and strange quarks in QCD 

      Peardon, Michael (Elsevier, 2019)
      The energy spectrum of a system containing a static quark anti-quark pair is computed for a wide range of source separations using lattice QCD with Nf=2+1 dynamical flavours. By employing a variational method with a basis ...