Pure & Applied Mathematics (Theses and Dissertations)
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Homotopical and effective methods for associative algebras
(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
(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
(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 ... 
YangMills instantons on the taubNUT space and supersymmetric N=2 gauge theories with impurities
(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
(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 fourmanifolds without boundary. We focus on the DonaldsonWitten theory, that is the N = 2 topologically ...