Browsing Pure & Applied Mathematics by Title
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The 2 + 2 anisotropic Wilson gluon action with applications
(2004)A generalization of anisotropic lattices to include a 2+2 discretization is discussed. As a part of this program, we determine the oneloop correction to the gluon selfenergy and analyse the restoration of Lorentz ... 
A dynamical study of the chirally rotated Schrödinger functional in lattice QCD
(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
(Trinity College (Dublin, Ireland). School of Mathematics, 2008)In this thesis, we develop the Geometric Discretization formulation of DiracKahler 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
(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. Samestimulus spike trains display structural similarities, yet ... 
A nonperturbative study of the renormalisation of action parameters in anisotropic lattice QCD with applications to finite temperature QCD
(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
(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 ... 
Absolute bases, tensor products and a theorem of Bohr
(Instytut Matematyczny Polska Akademia Nauk, 1990) 
Actions of groups of birationally extendible automorphisms
(World Science Publishing, 1996)The origin of this work is found in the study of automorphisms of domains D in Cn, n > 1. For example, suppose for the moment that D is relatively compact and recall that in this case the group Aut(D) of all holomorphic ... 
The AdS(5) x S**5 superstring in lightcone gauge and its Bethe equations.
(Institute of Physics, 2006)We use the uniform lightcone gauge to derive an exact gaugefixed Lagrangian and lightcone Hamiltonian for the GreenSchwarz superstring in AdS5?S5. We then quantize the theory perturbatively in the near planewave ... 
The Ads/CFT spectrum via Integrabilitybased algorithms
(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 RiemannHilbert problem. ... 
Analytic Besov spaces and Hardytype inequalities in tube domains over symmetric cones
(2010)We give various equivalent formulations to the (partially) open problem about Lpboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between ... 
Analytic smearing of SU(3) link variables in lattice QCD
(American Physical Society, 2004)An analytic method of smearing link variables in lattice QCD is proposed and tested. The differentiability of the smearing scheme with respect to the link variables permits the use of modern Monte Carlo updating methods ... 
Anisotropic discretisations and practical alltoall propagators for lattice QCD
(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 ... 
An Anisotropic preconditioning for the Wilson fermion matrix on the lattice
(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 ... 
Antisymmetric tensor field on AdS(5)
(Elsevier, 1998)By using the Hamiltonian version of the AdSrCFT correspondence, we compute the twopoint Green function of a local operator in Ds4 Ns4 super YangMills theory, which corresponds to a massive antisymmetric tensor field of ... 
Approximation and convergence of formal CRmappings
(Oxford University Press, 2003)Let M ? CN be a minimal realanalytic CRsubmanifold and M? ? CN? a realalgebraic subset through points p ? M and p? ? M?. We show that that any formal (holomorphic) mapping f : (CN, p) ? (CN? , p?), sending M into M?, ... 
Aspects of ChernSimons theory
(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
(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 recentlyderived nonlinear models for shallow water waves are presented. In the first part ...