Pure & Applied Mathematics: Recent submissions

Now showing items 6-25 of 390

    • Modularity in Supersymmetric Gauge Theory 

      Furrer, Elias Raphael (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)
      In this thesis, we study the modularity and duality of Coulomb branches for a class of four-dimensional N=2 supersymmetric gauge theories. For pure N=2 super Yang-Mills theory with gauge group SU(2), the Coulomb branch can ...

    • Conformal Bootstrap and Black Holes in AdS/CFT 

      Karlsson, Johan Robin (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)
      In this thesis, we explore applications of the conformal bootstrap to holographic CFTs that are dual to theories of gravity in asymptotically Anti-de Sitter spacetimes. In particular, we consider correlation functions with ...

    • Automorphic Symmetries, String integrable structures and Deformations 

      Pribitoks, Antons (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)
      We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on ...

    • Characters, coadjoint orbits and Duistermaat-Heckman integrals 

      Shatashvili, Samson (2021)
      The asymptotics of characters of irreducible representations of a compact Lie group G for large values of the scaling factor k are given by Duistermaat-Heckman (DH) integrals over coadjoint orbits of G. This phenomenon ...

    • Jordan systems, bounded symmetric domains and associated group orbits with holomorphic and CR extension theory 

      Matthews, John Alphonsus (Trinity College (Dublin, Ireland). School of Mathematics, 2006)
      The first chapter will deal with the one to one correspondence between the positive hermitian Jordan triple systems and the bounded symmetric domains. We start by defining the various Jordan systems. Then we continue by ...

    • Coherent states and classical radiative observables in the S-matrix formalism 

      Gonzo, Riccardo (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)
      In this thesis, we study classical radiative observables perturbatively in terms of on-shell scattering amplitudes. In particular, we focus primarily on the two-body problem in gauge and gravitational theories by using an ...

    • A performance study of a template C++ class for parallel Monte Carlo simulations of local statistical field theories on a three dimensional lattice 

      Burke, Liam (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2020)
      In this thesis we investigate the performance properties of a template C++ class designed to run parallel Monte Carlo simulations of local statistical field theories on a three dimensional lattice. The generic nature of ...

    • TT deformations of non-relativistic models 

      Frolov, Sergey; Esper, Chantelle (2021)
      The light-cone gauge approach to TT¯¯¯¯ deformed models is used to derive the TT¯¯¯¯ deformed matrix nonlinear Schrödinger equation, the Landau-Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions ...

    • 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 ...

    • Conformal bootstrap and thermalization in holographic CFTs 

      Tadic, Petar (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)
      This thesis covers a number of topics in conformal field theories that are supposed to have gravity duals according to the AdS/CFT correspondence. We use the conformal bootstrap in the Regge and lightcone limits as the ...

    • 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 ...

    • 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 ...

    • THE CATLIN MULTITYPE OF SUMS OF SQUARES DOMAINS 

      AIDOO, NICHOLAS (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)
      Given a sum of squares domain of finite D'

    • Computational and mathematical aspects of Feynman integrals 

      HIDDING, MARTIJN (Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)
      This thesis covers a number of different research projects which are all connected to the central topic of computing Feynman integrals efficiently through analytic methods. Improvements in our ability to evaluate Feynman ...

    • From positive geometries to a coaction on hypergeometric functions 

      Britto, Ruth (2020)
      It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, ...

    • 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 ...