Postgraduate Theses in the School of Mathematics and Statistics

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)
Wei Wu Limitations of dynamic programming approach: singularity and time-inconsistency (Supervisor: Goldys B)
James Gregory A q-discrete analogue of the third Painleve equation and its linear problem (Supervisor: Joshi N)
Huon Wilson Computing fast and accurate convolutions (Supervisor: Keich U)

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)

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 PainlevĂ© 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)