Postgraduate Theses in the School of Mathematics and Statistics

Theses submitted in 2017

Louis Bhim Polynomial bounds for solutions to boundary value and obstacle problems with applications to financial derivative pricing (Supervisor: Kawai R)
Kamil Bulinski Interactions between ergodic theory and combinatorial number theory (Supervisor: Fish A)
Ting-Ying Chang On singular solutions of weighted divergence operators (Supervisor: Cirstea F)
Joshua Ching Singular solutions of nonlinear elliptic equations with gradient terms (Supervisor: Cirstea F)
Shila Ghazanfar Statistical approaches to harness high throughput sequencing data in diverse biological systems (Supervisor: Yang J)
Thomas Porter A higher order analysis of sparse normal mixtures (Supervisor: Stewart M)
Kerry-Lyn Roberts Geometric singular perturbation theory and averaging: Analysing torus canards in neural models (Supervisor: Wechselberger M)
Pieter Roffelsen On the global asymptotic analysis of a q-discrete Painleve equation (Supervisor: Joshi N)
Joachim Worthington Stability theory and Hamiltonian dynamics in the Euler ideal fluid equations (Supervisor: Dullin H)
Philip Bos On Ramanujan's tau-function, modular forms and Hecke operators (Supervisor: Parkinson J)

Theses submitted in 2016

Michael Barwick Morse classification of low order jet spaces (Supervisor: Paunescu L)
Matthew Chan Mathematical modelling of dispersal and evolution of life-history traits in biological populations (Supervisor: Kim P)
John Mitry A geometric singular perturbation approach to neural excitability (Supervisor: Wechselberger M)
Ross Ogilvie Deformations of harmonic tori in \(S^3\) (Supervisor: Carberry E)
Dario Strbenac Novel preprocessing approaches for omics data types and their performance evaluation (Supervisor: Yang J)
Wei Wu Limitations of dynamic programming approach: singularity and time-inconsistency (Supervisor: Goldys B)
Huon Wilson Computing fast and accurate convolutions (Supervisor: Keich U)
James Gregory A q-discrete analogue of the third Painleve equation and its linear problem (Supervisor: Joshi N)
Andrew Swan Global statistics of banded random matrices and the Poisson/Gaudin-Mehta conjecture (Supervisor: Olver S)

Theses submitted in 2015

Alex Chalmers Mathematical modelling of atherosclerosis (Supervisor: Myerscough MR)
Gnanadarsha Dissanayake Advancement of fractionally differenced Gegenbauer processes with long memory (Supervisor: Peiris S, Wang Q and Proietti T)
Matthew Fitzpatrick Multi-regime models involving Markov chains (Supervisor: Stewart M)
Kaushala Jayawardana Prognostic methods for integrating data from complex diseases (Supervisor: Yang JH)
Kevin Murray Improved monotone polynomial fitting with applications and variable selection (Supervisor: Mueller S)
John Nakhoul The Kahler-Ricci flow on Riemann surfaces (Supervisor: Carberry E)
Danya Rose Geometric phase and periodic orbits of the equal-mass, planar three-body problem with vanishing angular momentum (Supervisor: Dullin HR)
Andrew Stephan Convection driven dynamos in rotating spheres (Supervisor: Ivers DJ)
Silvio Tarca Regulatory capital modelling for credit risk (Supervisor: Rutkowski M)
William Tong Coupled rigid body dynamics with application to diving (Supervisor: Dullin HR)
Montek Gill Representations of the fundamental groups of triangulated 3-manifolds (Supervisor: Tillmann S)
Michael Hendriksen Minimal permutation representations of classes of semidirect products of groups (Supervisor: Easdown D)
Damian Sercombe A family of uniform lattices acting on a Davis complex with a non-discrete set of covolumes (Supervisor: Paunescu L)

Theses submitted in 2014

Alexander Badran Arbitrage-free models for VIX and equity derivatives (Supervisor: Goldys B and Rutkowski M)
Clinton Boys Alternating quiver Hecke algebras (Supervisor: Mathas A)
Alice Dong Bayesian analysis of reserving models and applications (Supervisor: Chan JS and Peters G)
Darren Engwirda Locally optimal Delaunay-refinement and optimisation-based mesh generation (Supervisor: Ivers DJ)
John Maclean Numerical multiscale methods for ordinary differential equations (Supervisor: Gottwald G)
Inga Samonenko Nonparametric permutation test statistics and their saddlepoint approximations (Supervisor: Robinson J)
Duncan Sutherland Numerical study of vortex generation in bounded flows with no-slip and partial slip boundary conditions (Supervisor: Macaskill C)
Nicole Sutherland Algorithms for Galois extensions of global function fields (Supervisor: Donnelly S and Fieker C)
Emi Tanaka Statistical methods for improving motif evaluation (Supervisor: Keich U)
Garth Tarr Quantile based estimation of scale and dependence (Supervisor: Weber NC and Mueller S)
Victor Vera Ruiz Recoding of Markov processes in phylogenetic models (Supervisor: Robinson J)
Theodore Vo Geometric singular perturbation analysis of mixed-mode dynamics in pituitary cells (Supervisor: Wechselberger M)
Gareth White Algorithms for Galois group computations over multivariate function fields (Supervisor: Donnelly S and Fieker C)
Chong You Model selection and estimating degrees of freedom in Bayesian linear and linear mixed models (Supervisor: Mueller S and Ormerod JT)

Theses submitted in 2013

Natalie Aisbett Gamma polynomials of flag homology spheres (Supervisor: Henderson A)
Nigel Chan Uniform convergence on non-linear cointegrating regression (Supervisor: Wang Q)
Ivan Guo Competitive multi-player stochastic games with applications to multi-person financial contracts (Supervisor: Rutkowski M)
Philip Howes Geometry of Painleve equations and birational maps (Supervisor: Joshi N)
Ellis Patrick Statistical methods for the analysis and interpretation of RNA-Seq data (Supervisor: Yang JH)
Yinan Zhang p-adic verification of class number computations (Supervisor: Watkins M and Fieker C)
Matthew Gibson Graded decomposition numbers in type A (Supervisor: Mathas A)
Nicholas Wilson Dyson-Schwinger equations in quantum electrodynamics at finite temperature (Supervisor: Zhang R and Ivers D)

Theses submitted in 2012

Samuel Butler Inverse scattering transform method for lattice equations (Supervisor: Joshi N)
Alex Fun Raising operators, recurrences and the Littlewood-Richardson polynomials (Supervisor: Molev AI)
Igor Geninson Option pricing in composite volatility models (Supervisor: Buchen PW)
Hamish Ivey-Law Algorithmic aspects of hyperelliptic curves and their Jacobians (Supervisor: Kohel DR)
Ge Li Integral basis theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of type A (Supervisor: Mathas A)
Libo Li Random times and enlargements of filtrations (Supervisor: Rutkowski M)
Erwin Lobo Modelling the role of interclonal cooperativity during early carcinogenesis (Supervisor: Myerscough MR)
Roy Nawar On pricing and hedging of commodity derivatives and other hybrid products: theories and empirical implementations (Supervisor: Ivers DJ)
Marten Ting Asymptotic techniques and stochastic volatility in option pricing problems (Supervisor: Weber NC)
Jennifer Wilcox Some aspects of non parametric maximum likelihood for normal mixtures (Supervisor: Stewart M)
George Papadopoulos Semi-global symplectic invariants of the Euler top (Supervisor: Dullin HR)
Graham White Covolumes of latticies in automorphism groups of trees and Davis complexes (Supervisor: Thomas A)

Theses submitted in 2011

Anna Campain Challenges associated with clinical studies and the integration of gene expression data. (Supervisor: Yang YH and Mueller S)
James Edwards Decision making by collective intelligences (Supervisor: Myerscough MR)
Ian Gregory Large scale simulations in mathematical finance, with application to asymptotic statistics, pairs trading and CPPI (Supervisor: Ewald CO)
Justin Koonin Topology of eigenspace posets for unitary reflection groups (Supervisor: Lehrer GI)
Jonathan Kusilek On representations of affine Hecke algebras (Supervisor: Lehrer GI)
Lewis Mitchell Incorporating climatological information into ensemble data assimilation (Supervisor: Gottwald GA)
Parinya Sa Ngiamsunthorn Domain perturbation for parabolic equations (Supervisor: Daners D)
Allan Steel Construction of ordinary irreducible representations of finite groups (Supervisor: Cannon JJ)
Joanna Wang Bayesian analysis of stochastic volatility models: Modelling and application (Supervisor: Chan JS)
Justin Wishart Nonparametric estimation of change-points in derivatives (Supervisor: Weber NC)
Michael Barwick The Newton polygon and the Puiseux characteristic (Supervisor: Paunescu L)
Pamela Guzman Dispersive regularisations for the inviscid Burgers equation (Supervisor: Gottwald GA)
Connie Lam Geometric process models for financial time series (Supervisor: Chan JS)

Theses submitted in 2010

John Bourke Codescent objects in 2-dimensional universal algebra (Supervisor: Lack S)
Xiang Fu Root systems and reflection representations of Coxeter groups (Supervisor: Howlett RB)
Thomas Fung Tail dependence and mixing in the variance gamma and related models (Supervisor: Seneta E)
Sebastian Hermann Numerical investigation of the large core limit of spiral waves in excitable media (Supervisor: Gottwald G)
Ziad Jomaa The CASL method for vortex flows in irregularly shaped domains and the numerical solution of the Poisson equation (Supervisor: Macaskill C)
Tim Kyng Application of Black Scholes exotic option pricing theory to real options and executive share options (Supervisor: Buchen P/Weber NC/Konstandatos O)
Anna Ougrinovskaia Mathematical models of atherosclerosis (Supervisor: Thompson RS)
Neil Saunders Minimal faithful permutation representations of finite groups (Supervisor: Easdown D)
Wai Wan Extensions of the Poisson geometric process model with applications (Supervisor: Chan JS)

Theses submitted in 2009

Alhaji Bachtiar A study of planar dynamos and related issues (Supervisor: James RW)
Richard Finlay The variance gamma (VG) module with long range dependence (Supervisor: Seneta E)
James Kennedy On the isoperimetric problem for the Laplacian with Robin and Wentzell boundary conditions (Supervisor: Daners D)
Tegan Morrison Asymptotics of higher order Painleve equations (Supervisor: Joshi N)
Van Nguyen \(W\)-graphs for Hecke algebras (Supervisor: Howlett RB)
Yang Shi \(q\)-Discrete Painleve Equations and the Associated Linear Problems (Supervisor: Joshi N)
Tony Vassallo New models for pricing credit deriivatives (Supervisor: Buchen PW)
Ley Wilson \(Q\)-curves with complex multiplication (Supervisor: Kohel DR)
David Kelly On the Topology of Synchrony Optimised Networks (Supervisor: Gottwald G)
Michael Sun Orbits on the enhamced and exotic nilpotent cone (Supervisor: Henderson A)
Katharine Turner Willmore Tori in \(S^3\) (Supervisor: Carberry E)
Grad Dip:
Jong-Wook Son  (Supervisor: )

Theses submitted in 2008

David Gruenewald Explicit algorithms for Humbert surfaces (Supervisor: Kohel DR)
Mike Hay Discrete Lax pairs, reductions and hierarchies (Supervisor: Joshi N)
Kevin Ho Shon Real estate leases and real options (Supervisor: Buchen PW)
Mark Hopkins Quantum affine algebras: quantum Sylvestor theorem, skew modules and centralizer construction (Supervisor: Molev AI)
Shakti Menon Bifurcation problems in chaotically stirred reaction-diffusion systems (Supervisor: Gottwald G)
Yunchuan Yin \(W\)-graph representations for Coxeter groups and Hecke algebras (Supervisor: Howlett RB)
Stephen Enright-Ward CM proofs for elliptic curves over number fields (Supervisor: Kohel DR)
John Hornibrook Combustion waves in solid and viscous fuels (Supervisor: Gottwald G and Balasuriya S)

Theses submitted in 2007

Lucy Gow Yangians of Lie Superalgebras (Supervisor: Molev AI)
Mauro Grassi The isomorphism problem for a class of finitely generated Coxeter groups (Supervisor: Howlett RB)
Matthew Hardman Maximum entropy and its application to option pricing. (Supervisor: Buchen PW)
Vivek Jayaswal General Markov Models for Nucleotide Sequence Evolution (Supervisor: Robinson J)
Chris Ormerod Associated linear theory of ultradiscrete Painlevé equations (Supervisor: Joshi N)
Brad Roberts On Bosets and Fundamental Semigroups (Supervisor: Easdown D)
Karl Rodolfo A comparative study of American option valuation and computation (Supervisor: Buchen PW)
Timothy Schaerf On contour crossings in countour-advective simulations of geophysical fluid flows (Supervisor: Macaskill CC)
Ben Wilson Representations of infinite-dimensional Lie Algebras (Supervisor: Molev AI/Futorny VM)
Shona Yu The Cyclotomic Birman-Murakami-Wenzl Algebras (Supervisor: Howlett RB)
James Edwards Modelling Chemical Communication in Neuroglia (Supervisor: Gibson WG)

Theses submitted in 2006

Alistair Merrifield An investigation of mathematical models for animal group movement, using classical and statistical approaches (Supervisor: Myerscough M)
Peter O'Sullivan The generalised Jacobson-Morosov theorem (Supervisor: Lehrer GI)
Devindri Perera Saddlepoint approximation methods in the analysis of panel time series data (Supervisor: Peiris MS)
Leah Ratliff The alternating Hecke algebra and its representations (Supervisor: Mathas AP)
Gregory White Enumeration-based algorithms in linear coding theory (Supervisor: Cannon JJ)

Theses submitted in 2005

Faisal Ababneh Models and estimation for phylogenetic trees (Supervisor: Robinson J)
Sacha Blumen Quantum superalgebras at roots of unity and topological invariants of three-manifolds (Supervisor: Zhang RB)
James East On monoids related to braid groups and transformation semigroups (Supervisor: Easdown D)
Hai Ho On Hilbert modular forms (Supervisor: Lai K)
Krishnasamy Muraleedaran Investigation of normalizers of parabolic subgroups of irreducible unitary reflection groups (Supervisor: Taylor DE)
James Parkinson Buildings and Hecke Algebras (Supervisor: Cartwright DI)
Benjamin Smith Explicit endomorphisms and correspondences (Supervisor: Kohel D)
Annie Tjetjep Estimation under GNVM for Financial Data (Supervisor: Seneta E)
Stewart Wilcox Cellularity of Twisted Semigroup Algebras of Regular Semigroups (Supervisor: Easdown D)

Theses submitted in 2004

Noelle Antony On Singular Artin Monoids (Supervisor: Easdown D)
William Bertram Modelling asset dynamics via an empirical investigation of Australian stock data (Supervisor: Buchen PW)
Beatrice Bleile Poincare Duality Pairs of Dimension Three (Supervisor: Hillman JA)
Feng Dai Approximation of real smooth functions (Supervisor: Brown G)
Michael Kemp Geometric Seifert 4-manifolds with aspherical bases (Supervisor: Hillman JA)
Otto Konstandatos A new framework for pricing barrier and lookback options (Supervisor: Buchen PW)
Greg Woodbury Modelling emergent properties of the visual cortex (Supervisor: Gibson W)
Ruxue Yu Fixed point calculations on cones (Supervisor: Dancer EN)
Ponnuthurai Ainkaran Analysis of some linear and nonliner time series models (Supervisor: Peiris MS)
Henrik Latter Topics in Kinematic Dynamo Theory (Supervisor: Ivers D)
Stephen Meagher Cusps of Hilbert modular surfaces and 4-folds (Supervisor: Paunescu L)

Theses submitted in 2003

Greg Lemon Mathematical modelling of some aspects of intracellular second messenger signalling (Supervisor: Gibson W)
Emmanuel Letellier Fourier transforms of invariant functions on a finite Lie algebra (Supervisor: Lehrer GI/Michel J)
Jonathan Turner Signal processing applied to satellite magnetic data (Supervisor: Ivers D)
Lei Zhang The interaction effect of self-heating packages in a shipping container (Supervisor: Macaskill CC)

Theses submitted in 2002

Michael Stewart Asymptotic methods for tests of homogeneity finite mixture models (Supervisor: Robinson J)
Peter Zeitsch Symmetry groups for hypergeometric partial differential equations (Supervisor: Fackerell ED/Cosgrove C)
Alhaji Bachtiar Numerical investigation of the planar flow anti-Dynamo theorem (Supervisor: James RW)
Katherine Courtney Asymptotics for estimators of the shape parameter for the negative binomial distribution (Supervisor: Weber NC)
Patrick Jordan On biordered sets, including an alternative approach to fundamental regular semigroups (Supervisor: Easdown D)
John McCloughan Evolving synoptic maps of the solar magnetic field (Supervisor: Durrant C)
Fai Tsang Gelfand-Tsetlin bases for representations of general linear algebras (Supervisor: Molev A)

Theses submitted in 2001

Melissa Cox Models for self-organisation in insect societies. (Supervisor: Myerscough M)
William Franzsen Automorphisms of Coxeter groups (Supervisor: Howlett RB)
Andrew Hayen Some exact results for Poisson Voronoi tesselations (Supervisor: Quine MP)
Christopher Macmeikan The equivariant cohomology of toral complements (Supervisor: Lehrer GI)
Usha Sridhar Models of associative memory (Supervisor: Gibson W)
Ilknur Tulunay Cuspidal modules of finite general linear groups. (Supervisor: Howlett RB)
Andrew Vincent Mathematical analyses of ant-based systems. (Supervisor: Myerscough M)

Theses submitted in 2000

Ruth Corran On monoids related to braid groups (Supervisor: Easdown D)
Susan Evans-Riley On the derived length of finite, graded Lie rings with prime-power order, and groups with prime-power order (Supervisor: Gagen T/Newman M)
Hossein Farajollahi Time and observables in general relativity and parametrised theories (Supervisor: Luckock H)
Rungao Jin Some aspects of saddlepoint approximations for non-parametric statistics (Supervisor: Robinson J)
Rupert Littlewood Hierarchies and asymptotics of Painlevé type equations (Supervisor: Cosgrove C)
Hamish Meffin Two neural models-I A cortical memory model, and II Networks of leakless integrate-and-fire neurons (Supervisor: Gibson W)
David O'Toole Self-organised criticality in lattice swarms (Supervisor: Myerscough M)
Kevin Ho Shon Signal processing of dynamic positron emission tomography studies (Supervisor: Buchen PW)

Theses submitted in 1999

Robin Cobb Infra-solvmanifolds of dimension four (Supervisor: Hillman JA)
Clare Coleman Circle decompositions of rings, in particular, Munn rings (Supervisor: Easdown D)
Amitavo Islam Constructing free distributive categories (Supervisor: Walters RFC)
George Scoufis An application of the inverse scattering transformation to some nonlinear integro-differential equations (Supervisor: Cosgrove C)
Ziad Jomaa Analysis of equivalent circuits for voltage-clamp experiments (Supervisor: Gibson W)
Krishnasamy Muraleedaran Primitive unitary reflection groups with non-abelian fitting subgroup (Supervisor: Taylor DE)

Theses submitted in 1998

Abdulrahman Abdulaziz Symmetric attractors of equivariant maps on the torus. (Supervisor: Dancer EN)
Robert Cameron Axisymmetric magnetoconvection (Supervisor: Galloway DJ)
Clare Chapman Investigation of synchronisation in a mathematical model of cortical function (Supervisor: Gibson W / Wright J)
James Clark The dynamical behaviour of a rotating thread (Supervisor: Fraser WB)
Diana Combe Distance transitive directed graphs and multiplicity free primitive permutation representations with almost no real irreducible constituents (Supervisor: Taylor DE)
Alex Davyskib Gyroscopic stabilization of a spacecraft with two antennas attached (Supervisor: Winch DE)
Thomas Gillespie The stochastically subordinated Poisson normal process for modelling financial assets (Supervisor: Buchen PW/Edelman DC)
Philipp Hofflin Intermediate alpha-omega geodynamo models (Supervisor: James RW)
Brett McElwee Locally ordered bisets (Supervisor: Easdown D)
Tim Svenson Groups acting simply transitively on \(\tilde A_n)\ buildings (Supervisor: Cartwright DI)
Diana Warren The Frobenius-Harper Technique in a General Recurrence Model (Supervisor: Seneta E)
Henry Weld On categories of asynchronous circuits (Supervisor: Walters RFC)
Gregory Cave The stability of the two-for-one twister balloon with yarn elasticity (Supervisor: Fraser WB)
Vinsenia Suhana Comparison of variance estimates for parameter estimators in Cox regression (Supervisor: Weber NC)

Theses submitted in 1997

Ronen Ben Hador Seismic surface wave computations in non-uniform layered media (Supervisor: Buchen PW)
Jerome Blair The Poincare polynomials of the complex reflection groups (Supervisor: Lehrer GI)
Damien Burtonclay On the determination of the internal solar rotation profile through helioseismology (Supervisor: Wilson PR)
John Crisp Three topics in topology and group theory (Supervisor: Hillman JA)
Robert Gates On extensive and distributive categories (Supervisor: Walters RFC)
Stephen Goulter The global semi-diurnal atmospheric tides S2, L2 and N2 (Supervisor: Winch DE)
David Jackson On nilpotent orbits of type \(G_2\) (Supervisor: Lehrer GI)
Rowan Kemp Combinatorics on Fibonacci Lattices (Supervisor: Wehrhahn KH)
Simon Ku Tests based on sample partial autocorrelations (Supervisor: Seneta E)
Ben Langton Lie symmetry techniques for exact interior solutions of the Einstein field equations for axially symmetric, stationary, rigidly rotating perfect fluids (Supervisor: Fackerell ED)
Joseph Lau Growth of a Class of Inverse Semigroups (Supervisor: Easdown D/Howlett RB)
Olga Podvigina Spatially periodic steady and evolutionary solutions to the three dimensional Navier-Stokes equation and ABC forcing (Supervisor: Galloway DJ)
Richard Rannard Normal surfaces and the topology of three-manifolds (Supervisor: Hillman JA)
Jennifer Law Markov models for linear growth models (Supervisor: Quine MP)

Theses submitted in 1996

Tu Chen Multivariate Bonferroni-type inequalities and optimality (Supervisor: Seneta E)
Piergiulio Katis Categories and bicategories of processes (Supervisor: Walters RFC)
Mark Leeming Computing left Kan extensions using generalizations of the Todd-Coxeter procedure (Supervisor: Walters RFC)
Chunsheng Ma Asymptotic approximations for sample quantiles (Supervisor: Robinson J)
Andrew Solomon Concrete monoids, automata and the catalan construction (Supervisor: Easdown D)
Remy Van de Ven Estimation in mixed Poisson regression models (Supervisor: Weber NC)
Richard Hunt An investigation into the variance and bias of some lag windows spectral density (Supervisor: Peiris MS/Weber N)
Ivan Le Creurer Algebraic presentation of categories with certain limits over the category of graphs (Supervisor: Kelly GM/Sun SH)

Theses submitted in 1995

Ping Cao Wave scattering from rough surfaces (Supervisor: Macaskill CC)
John Graham Modular representations of Hecke algebras and related algebras (Supervisor: Lehrer GI)
Oliver Jones On the geometry of varieties of invertible symmetric and skew-symmetric matrices (Supervisor: Dimca A)
Timothy Lavers The Vine monoid and its associated transformation monoids (Supervisor: Easdown D)
Qing Zhou Poincare polynomials for projective hypersurfaces (Supervisor: Dimca A)

Theses submitted in 1994

Brigitte Brink On root systems and automacity of Coxeter groups (Supervisor: Howlett RB)
Neil Holbrook Temperature variability in the Southwest Pacific Ocean (Supervisor: Macaskill CC)
Wafaa Khalil Functional processors with applications to imperative programming (Supervisor: Walters RFC)
John Thatcher The chromospheres of K dwarf stars (Supervisor: Rees/Durrant CJ)
Peter Thomson Statistics models of synaptic transmission (Supervisor: Robinson J)
Jan Hansen Symmetry analysis of kinematic magnetic induction equations (Supervisor: Fackerell ED)
Chris Oliwa A new approach to the quantization of Bianchi Class A models in supergravity (Supervisor: Luckock HC)
Walid Ramadan Half spin representations and the Klein correspondence (Supervisor: Taylor DE)
Phaedra Ravier-Hay Observation and modelling of the mixed layer in the western tropical pacific warm (Supervisor: Ivers DJ)