The educational staff the following have indicated their readiness to supervise thesis research. In some instances specific topics are listed, while in some cases an over-all market is indicated.

Prospective students should you can approach these staff people to go over the potential of alternative topics to individuals right here, or indeed every other employee to go over possible thesis topics. Further suggestions for possible research topics can also be acquired in the Graduate Studies web site.

## Topics and Regions of Interest

Multivariate Approximation Theory of the applied variety. Particularly thinking about the maths and statistical analysis underlying such methods, having a view to some wealthy number of applications for example Computer Aided Geometric Design, Image Processing, Natural Resource Modelling and Neural Nets.

Constructive mathematics may be the term put on mathematics that is dependant on intuitionistic Zermelo–Fraenkel set theory and uses only intuitionistic logic. This logic was formulated by Heyting in 1930, and captures the essence of the algorithmic method of mathematical proof. One outstanding gap within the constructive research literature is the topic of differential manifolds and Riemannian geometry no–one has yet created an acceptable constructive perception of “differential manifold”, not to mention tackled the truly hard problem of developing the idea, through tangent bundles, vector fields, and Lie groups, towards Riemannian geometry. Since Einstein’s General Theory of Relativity is dependant on classical Riemannian geometry, a constructive growth and development of the second is important before we are able to hope to supply a constructive mathematical method of gravitation and cosmology.

The purpose of this PhD project is first to make a constructively helpful meaning of “differential manifold”, after which to build up, constructively, the basic principles of Riemannian geometry. Ideally, we’ll produce conditions to which it’s possible to construct geodesics on this type of manifold this will probably be very hard, because the classical existence proof uses general results about continuous functions that aren’t relevant constructively and don’t even give any clues on how to create a constructive existence proof.

Various topics within the theory of operators and operator algebras on the Hilbert space, investigated constructively.

The idea of the apartness space appears to deal with great promise for any effective constructive growth and development of general topology. There are many facets of the idea of apartness spaces that will make good doctorate research, which would take part in a task involving co–workers in Germany, Japan, and Romania.

This project involves searching at optimal survey designs for monitoring alterations in animal population abundance, particularly, vertebrates unwanted pests species. The work may incorporate some field work.

Statistics on spatial patterns will be employed to model optimal network designs for ecological monitoring.

Facets of adaptive sampling will be employed to develop optimal designs.

The practicality of utilizing existing possum–monitoring data for estimating population density surfaces which permit for spatial and temporal variation by the bucket load is going to be investigated.

- Visualization and also the learning and teaching of mathematics.
- Technology in mathematics education.

Background: Its these topics you need to know something about research methods in education (for instance, from EDUC320).

- I’m pleased to discuss any proposal which uses students’s particular background or interests.

I’m also prepared to consider proposals about Masters in algebra (ring theory or straight line algebra).

Differential equations might be considered a range (i.e. a surface) inside a high dimensional space known as the jet bundle. The benefit of this method is it enables someone to use geometric insights to look at the qualities of person solutions and also to analysis connections between different teams of differential equations. The computations this field requires only have become viable using the development during the last decade of efficient algebraic computing engines like Walnut and MATHEMATICA. Research in this region that i’m ready to supervise include symmetry investigations of specific equations or classes of equations differential invariants, their computation and application to problems including the pc recognition of objects extensions to differential-difference equations and also to the introduction of efficient Walnut code to apply the various computations this field requires.

Topics in Computational Statistics and Bayesian Statistics, including applications in functional genomics and gene expression analysis, medical/biological/engineering model verification, and signal and image processing.

- Historic Episode: the historic and mathematical analysis of the significant episode within the good reputation for mathematics.
- Historic Work: the textual and mathematical analysis of the historic work, in both translation or original language (British, Cuneiform, Greek, Latin, Sanskrit, Arabic, French).
- Historic Theme: study regarding various mathematical styles in the good reputation for mathematics, including (but in no way restricted to) mathematical notation and symbolic reasoning, utilization of diagrams, mathematical tables, parallel insights, approximation techniques, and mathematical astronomy, for instance.
- Ethnomathematics

Pleased to supervise various topics in philosophy of mathematics jointly with colleagues in philosophy.

- Weed risk assessment and control.
- Modelling spread of invasive plant species.
- Modelling the first stages of coronary artery disease.

Phylogenetics may be the renovation and analysis of phylogenetic trees and systems according to inherited characteristics.

Possible Masters and PhD projects include

Mathematical phylogenetics connected with reticulate evolution.

Combinatorial problems in supertree construction.

Matroids are exactly the structures that underlie the answer of numerous combinatorial optimisation problems. These complaints include scheduling and timetabling, and locating the minimum price of a communications network between metropolitan areas. Furthermore, matroid theory unifies the notions of straight line independence in straight line algebra and forests in graph theory along with the notions of duality for graphs and codes.

Possible Masters and PhD projects include

- Matroid connectivity and structure.
- Matroid representation.

- Combinatorial/topological/geometric facets of just transformative trees.
- Ordinal methods in phylogeny.
- Figuring out record consistency of minimum evolution methods.
- Other topics: Population genetics rates of evolution transformative game theory, Modelling directional evolution, Abstract origin–of–life models, genomic analysis.

- Modelling hybridization and representation of transformative history by digraphs.
- Combinatorial/topological/geometric facets of just transformative trees.

Interpolating systems are groups of curves because both versions is distinctively based on a particular quantity of its points. One of many qualities every interpolating system has (analytic, geometric and statistical) the main focus is around the geometric aspect.

Possible Masters and PhD projects cope with

- Construction of interpolating systems
- Characterisation of certain interpolating systems by configurational conditions
- Resolution of the automorphism categories of interpolating systems and classification of the very most homogeneous ones
- Characterisation of certain interpolating systems by categories of transitive automorphisms
- Applications to secrete discussing schemes.

I am also prepared to consider proposals in algebra, combinatorics or topology.

- Mathematical Wave propagation for inverse and direct problems, both statistical and theoretical aspects.
- Mathematical Biology staring at the mathematical facets of cellular secretion from corticotroph cells within the pituitary.

In the Masters or PhD levels, I’m able to propose topics around the Potential Theory of partial differential equations. The equations could be elliptic or parabolic, with constant or variable coefficients. For that Potential Theory of Laplace’s equation, the prototype for those others, begin to see the books “Introduction to Potential Theory” by L.L.Helms (Wiley, 1969), and “Classical Potential Theory” by D.H.Armitage S.J.Gardiner (Springer, 2001).

In the Masters level, I’ll also consider supervising any subject of the analytic nature, whether it is in analysis, topology, fuzzy topology, or whatever. So if you have a concept, run it past me.