School of Mathematics
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Pure & Applied Mathematics
Pure & Applied Mathematics
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Computational and mathematical aspects of Feynman integrals
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2020)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
(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 oneloop Feynman integrals in dimensional regularization, ... 
A family of compact strictly pseudoconvex hypersurfaces in C^2 without umbilical points
(2018)We prove the following: For ϵ>0, let Dϵ be the bounded strictly pseudoconvex domain in ℂ2 given by (logz)2+(logw)2<ϵ2. The boundary Mϵ:=∂Dϵ⊂ℂ2 is a compact strictly pseudoconvex CR manifold without umbilical ... 
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 ...