Note: Where students have a personal web page, a link is provided.
Student Information |
Thesis Title and Description |
Student: Claire Edwards
Supervisor: Brian Davey
Co-supervisor: Marcel Jackson |
I am investigating the notion of standardness of finite topological algebras. One of the methods I am using is the concept of finitely determined syntactic congruences. This allows topological results to be derived via purely algebraic means. |
Student: Paul Martin
Supervisor: Geoff Prince
Co-supervisor: Peter Stacey |
Title: Geometric analysis of flows in R3.
Description: I am investigating the use of the shape map Az for the geometric analysis of flows in R3. The Frenet frame field is being used as a basis due to its informative nature and its connection with the shape map. This may lead to insight into the behavior of chaotic R3 flows. |
Student: Tom Poole
Supervisor: Grant Cairns
Co-supervisor: Yuri Nikolayevsky |
Title: Einstein manifolds of low dimension.
Description: I am investigating the classification of Einstein manifolds of dimension 3 and 4. |
Student: Korrakot Chartarrayawadee
Supervisor: Grant Cairns
Co-supervisor: Brian Davey |
Title: Sprouts on surfaces.
Description: I am investigating various combinatorial and topological properties of Conway's game of Sprouts, played on arbitrary oriented and non-oriented surfaces. |
Student: Tony Nielsen
Email: A.Nielsen@latrobe.edu.au
Supervisor: Grant Cairns
Co-Supervisor: John Banks |
Title: Chaotic dynamics of continuous actions of discrete
groups.
The object is to study the chaotic dynamics of continuous actions of discrete groups on topological spaces. |
Student: Todd Niven
Supervisor: Brian Davey.
Co-supervisor: Narwin Perkal |
Title: The full versus strong problem in the theory of natural dualities.
Description: I am investigating the notions of Full and Strong Duality in the Theory of Natural Dualities and whether they are equivalent (which we know not to be the case for dualities at the finite level). |
Student: Priscilla Tse
Email: pptse@students.latrobe.edu.au
Supervisor: Reinout Quispel
Co-Supervisor: Dave McLaren |
Title: Geometric Integration
.
In geometric integration, methods have been developed to preserve certain properties of the dynamical system. Examples include the preservation of symmetries, volume in phase space, or symplecticity. However, it remains unclear whether one can preserve two or more geometric properties simultaneously. I am currently investigating the possibilities of constructing such numerical integrators; in particular, searching for methods which can preserve both volume and symmetries. |
Student: Michael Jerie
Email: M.Jerie@latrobe.edu.au
Supervisor: Geoff Prince
Co-Supervisor: Graham Byrnes |
Title: The Geometry of Second Order ODE's.
I'm investigating the behavior of solutions of 2nd order ode's using some differential geometric gagetry available in tangent bundle geometry. For example when is it possible to deduce solutions form compact submanifolds without explicitly solving the de.
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Student: Apostolos Iatrou
Email: A.Iatrou@latrobe.edu.au
Supervisor: Reinout Quispel
Co-Supervisor: John Roberts
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Title: Integrable Mappings.
Description: My research is primarily concerned with integrable mappings, i.e. mappings which possess a sufficient number of constants of motion or integrals. I have been looking into ways of extending known integrable mappings and/or constructing new ones. I am also interested in integrating such mappings.
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Student: Jonathan Aldridge
Email: J.Aldridge@latrobe.edu.au
Supervisor: Geoff Prince
Co-Supervisor: Graham Byrnes |
Title: The solution to the inverse problem in the calculus of variations.
The inverse problem is the search for the existence and degeneracy of Lagrangian functions for a given second order differential system. I am looking for a way of extending Douglas's solution to this problem for 2-dimensions to a solution in at least 3-dimensions.
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Student: Darren Condon
Email: D.Condon@latrobe.edu.au
Supervisor: Alan Andrew
Co-Supervisor: Peter Stacey
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Title: The numerical solution of eigenvalue problems for differential operators.
Most methods of solving eigenvalue problems for differential operators suffer greatly for higher eigenvalues, but a technique of asymptotic correction has worked well to improve these methods, particularly for the higher eigenvalues. At present, theoretical estimates of the error seem to be larger than those found in practice, and some work needs to be done to sharpen the theoretical estimates. The range of examples on which the asymptotic correction technique may be used is also quite limited, and some way of extending it to other problems is being sought.
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Student: Jim Pettigrew
Supervisor: John Roberts
Co-supervisor: Reinout Quispel |
Title: A Computer Assisted Investigation of One Dimensional Discrete Dynamical Systems.
My research is motivated by a particular set of problems in discrete dynamical theory and abstract algebra. Linear modular maps defined over Zp and its p-adic extensions are perturbed in such a way as to render them, when expanded, resistant to "decoding" - i.e. not conjugate to linear - and possessive of a special periodic orbit structure - the maximal orbit of which occupies a suitably large proportion of the map's phase space.
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Student: James Scully
Supervisor: Reinout Quispel |
Title: Numerical Integration Methods and Rooted Trees.
I'm using rooted trees to study the properties of the family of numerical integrators known as Runge-Kutta methods. Runge-Kutta methods and exact solutions to ordinary differential equations can both be written as B-series, which involve rooted trees. By taking compositions of these B-series, it is possible to construct Runge-Kutta methods which are conjugate to methods that preserve important properties of the exact solution. This is important because preserving such properties often places restriction on the methods. For instance, symplectic methods, which preserve Hamiltonian structure, must be implicit. If a method is conjugate to symplectic it need not necessarily be implicit but may still possess many of the useful features of symplectic methods.
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Student: Suharsono
Supervisor: Reinout Quispel
Co-Supervisor: David McLaren |
Title: Dynamical Systems and Numerical Analysis: Integral Preserving Integration Methods for Ordinary Differential Equations.
The properties and performance of integral preserving integrators as dynamical systems have been studied analytically and numerically, in particular in Hamiltonian systems.
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Student: Jane Pitkethly
Supervisor: Brian Davey |
I am writing a PhD thesis entitled "Dualisability: unary algebras and beyond". It is based on some of my papers, which are available HERE.
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Student: Bradley Knox
Supervisor: Brian Davey
Co-Supervisor: Grant Cairns |
Title: Dualisability of finite semigroups.
The structure theory of certain semigroups is used to find natural dualities.
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Student: Rashed Talukder
Supervisor: Brian Davey
Co-Supervisor: Grant Cairns |
Title: Duality Theory with Applications to Lattice-Ordered Algebras.
I am working on the interface between Priestley dualities and natural dualities for algebras arising in non-classical logic. At the moment I am considering natural dualities, both single-sorted and multi-sorted, for finitely generated quasi-varieties and varieties of Heyting algebras.
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Omar Rojas
Jodie Smith