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Search the School of Mathematical Sciences
People matching "Mathematics of string theory"
Courses matching "Mathematics of string theory"
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Computational Mathematics III 
This course introduces numerical techniques for tackling mathematical problems and for assessing the accuracy of of the numerical results obtained. It uses methods appropriate to common mathematical models including algebraic equations, ordinary and partial differential equations and integrals. It discusses causes of numerical errors and ways to estimate the effects of those errors on the computed solution to a problem. It also gives practice in writing Matlab codes to implement numerical algorithms.
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Distribution Theory and PDEs
Topics in Analysis and Geometry
The the theory of distributions was developed by Laurent Schwartz,
for which he received the Fields Medal in 1950, and is considered
as being one of the revolutions in mathematics in the 20th century.
It is a powerful tool, with wide applications to mathematics and physics.
Distribution theory is accessible to a wide audience, including
mathematics students specializing in almost any area of mathematics and
also those specializing in mathematical physics.
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Engineering Mathematics 1
Mathematics is an essential tool for understanding and predicting engineering systems. This course consists of an introduction to differential equations, which are used to model deterministic systems, and basic probability and statistical methods, which are used to analyse random processes. Ordinary differential equations: First order, second order, series solutions. Fourier series for functions of arbitrary period, half range expansions, even and odd functions, complex form of Fourier series. Partial differential equations: heat equation, separation of variables, wave equation, Laplace's equation. Applications in boundary value problems. Probability and statistical methods: Sampling and probability, descriptive statistics, random variables and probability distributions, mean and variance, linear combinations of random variables. Statistical inference for means and proportions. Linear regression.
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Engineering Mathematics 2
Topics covered include: Vector calculus: vector fields, gradient, divergence and curl. Line, surface and volume integrals, integral theorems of Green Gauss and Stokes, with applications. Orthogonal curvilinear coordinates. Complex analysis: elementary functions of a complex variable, complex analytic functions, complex integrals, Taylor Series, Laurent Series, Residue Theorem. Laplace transforms of derivatives and integrals, applications to differential equations
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Industrial Mathematics III
In this course a number of real-world industrial case studies are presented. These case studies lead to mathematical models which involve differential equations. The differential equations are solved and the solutions analysed in order to provide an understanding of the particular industrial process under examination. The importance of mathematical modelling. Diffusion and advection and the equations that derive these physical processes. Fick's and Fourier's laws. Common boundary conditions for advection-diffusion problems. Newton cooling. Scaling of equations and basic dimensional analysis. A selection of case studies from the following. Each introduces a different concept or mathematical method. Continuous casting of sheet steel. This involves a Stefan condition for a moving boundary and the reduction of variables by the Boltzmann transformation to give the Boltzmann similarity solution of the heat equation. Water filtration by reverse osmosis, introducing invariance of equations and the method of stretching transformations to reduce a PDE problem to an ODE problem. Laser drilling. A Stefan condition is required for the moving boundary and the method of regular perturbations is introduced. Factory fires due to spontaneous ignition. This introduces bifurcation analysis. Furrow irrigation. The non-linear PDE describing the problem is transformed to a linear PDE by the Kirchoff transformation. Fourier series are used to solve the linear PDE.
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Information Theory
Five broad topics are addressed:
(1) the concepts of information and uncertainty;
(2) noiseless coding;
(3) stationary information sources;
(4) memoryless channels;
(5) group codes. Uncertainty, Shannon's uniqueness theorem,
properties of uncertainty, information, noiseless coding, unique
decipherability, instantaneous codes, Huffman constructions. Kraft's
theorem, McMillan's theorem, Shannon's first coding theorem, ideal
observer and maximum likelihood decision schemes, fundamental theorem
of coding, stationary sources, uncertainty of a source, Markov
sources, unifilar sources, uncertainty of a state. The asymptotic
equipartition property. Error correcting codes, parity check for
group codes, decoding parity check codes, cyclic codes, feedback shift
registers, Bose-Chaudhuri-Hocquenhem codes.
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Introduction to Financial Mathematics I
Algebra: Matrices and linear equations. Optimisation problems: solutions by graphical and algebraic methods.
Functions and Annuities: linear, quadratic, exponential and logarithmic functions; simple and compound interest, annuities and amortization of loans. Continuous rates of change and the derivative.
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Mathematics for Information Technology I
Discrete Mathematics: Sets, relations,
logic, graphs, mathematical induction and recurrence relations
(difference equations)
Probability: Sample spaces, events,
discrete random variables and distributions.
Information security and encryption: Elementary number
theory and the RSA algorithm - the most common public key encryption
system now in use.
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Mathematics IA
Calculus: Functions, including the
exponential and logarithmic functions; Integration - the definite
integral and the Fundamental Theorem of Calculus; methods of
integration, Numerical integration and applications of the definite
integral.
Linear Algebra: Matrices and systems of linear equations;
elementary matrices and the inverse; determinants; optimisation
problems and convex sets; subspaces, linear combinations and linear
independence; eigenvalues and eigenvectors; diagonalisation of
matrices.
More about this course...
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Mathematics IB
Calculus: Differential Equations; Limits, continuity, the Mean Value Theorem with applications to curve sketching and maxima and minima problems; Taylor polynomials, power series and Taylor series; calculus of two variables including partial derivatives, the directional derivative, tangent planes and local
maxima and minima.
Linear Algebra: Basis, dimension of subspaces of the real vector space R^n; orthonormal bases and the Gram-Schmidt
process; linear transformations; conics, quadric surfaces and polar cordinates; symmetric matrices and orthogonal diagonalisation.
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Mathematics IIM
Calculus: Taylor polynomials, power series
and Taylor series. Limits, continuity, the Mean Value Theorem with
applications to curve sketching and maxima and minima problems.
Linear Algebra: Subspaces, linear
combinations and linear independence; basis, dimension of subspaces;
orthonormal bases and the Gram-Schmidt process; symmetric matrices and
orthogonal diagonalisation; applications of linear algebra. Linear
transformations.
More about this course...
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Mathematics IMA
Calculus:
Functions, including the exponential, logarithmic and trigonometric
functions and their inverses. Differentiation - the derivative and
its applications; rules for differentiation and the derivatives of the
common functions.
Linear Algebra: Complex numbers and polynomial
equations. Vectors in two and three dimensions; Matrices and systems
of linear equations; the inverse of a square matrix; applications to
Markov chains; optimisation problems, and the Simplex Algorithm.
More about this course...
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Events matching "Mathematics of string theory"
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Stability of time-periodic flows 15:10 Fri 10 Mar 06 | G08, Mathematics Building, University of Adelaide | Prof. Andrew Bassom, School of Mathematics and
Statistics, University of Western Australia
Abstract...Time-periodic shear layers occur naturally in a wide
range of applications from engineering to physiology. Transition to
turbulence in such flows is of practical interest and there have been
several papers dealing with the stability of flows composed of a
steady component plus an oscillatory part with zero mean. In such
flows a possible instability mechanism is associated with the mean
component so that the stability of the flow can be examined using some
sort of perturbation-type analysis. This strategy fails when the mean
part of the flow is small compared with the oscillatory component
which, of course, includes the case when the mean part is precisely
zero.
This difficulty with analytical studies has meant that the stability
of purely oscillatory flows has relied on various numerical
methods. Until very recently such techniques have only ever predicted
that the flow is stable, even though experiments suggest that they do
become unstable at high enough speeds. In this talk I shall expand on
this discrepancy with emphasis on the particular case of the so-called
flat Stokes layer. This flow, which is generated in a deep layer of
incompressible fluid lying above a flat plate which is oscillated in
its own plane, represents one of the few exact solutions of the
Navier-Stokes equations. We show theoretically that the flow does
become unstable to waves which propagate relative to the basic motion
although the theory predicts that this occurs much later than has been
found in experiments. Reasons for this discrepancy are examined by
reference to calculations for oscillatory flows in pipes and
channels. Finally, we propose some new experiments that might reduce
this disagreement between the theoretical predictions of instability
and practical realisations of breakdown in oscillatory flows.
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Inconsistent Mathematics 15:10 Fri 28 Apr 06 | G08, Mathematics Building, University of Adelaide | Prof. Chris Mortensen
Abstract...The Theory of Inconsistency arose historically from a
number of sources, such as the semantic paradoxes including The Liar
and the set-theoretic paradoxes including Russell's. But these sources
are rather too closely connected with Foundationalism: the view that
mathematics has a foundation such as logic or set theory or category
theory etc. It soon became apparent that inconsistent mathematical
structures are of interest in their own right and do not depend on the
existence of foundations. This paper will survey some of the results
in inconsistent mathematics and discuss the bearing on various
philosophical positions including Platonism, Logicism, Hilbert's
Formalism, and Brouwer's Intuitionism.
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Mathematics of underground mining. 15:10 Fri 12 May 06 | G08, Mathematics Building, University of Adelaide | Prof. Hyam Rubinstein
Abstract...Underground mining infrastructure involves an
interesting range of optimisation problems with geometric
constraints. In particular, ramps, drives and tunnels have gradient
within a certain prescribed range and turning circles (curvature) are
also bounded. Finally obstacles have to be avoided, such as faults,
ore bodies themselves and old workings. A group of mathematicians and
engineers at Uni of Melb and Uni of SA have been working on this
problem for a number of years. I will summarise what we have found and
the challenges of working in the mining industry.
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Maths and Movie Making 15:10 Fri 13 Oct 06 | G08, Mathematics Building, University of Adelaide | Dr Michael Anderson
Abstract...Mathematics underlies many of the techniques used in
modern movie making. This talk will sketch out the movie visual
effects pipeline, discussing how mathematics is used in the various
stages and detailing some of the mathematical areas that are still
being actively researched.
The talk will finish with an overview of the type of work the speaker
is involved in, the steps that led him there and the opportunities for
mathematicians in this new and exciting area.
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Good and Bad Vibes 15:10 Fri 23 Feb 07 | G08, Mathematics Building, University of Adelaide | Prof. Maurice Dodson
Abstract...Collapsing bridges and exploding rockets have been associated with vibrations in resonance with natural frequencies. As well, the stability of the solar system and the existence of solutions of Schrödinger\'s equation and the wave equation are problematic in the presence of resonances. Such resonances can be avoided, or at least mitigated, by using ideas from Diophantine approximation, a branch of number theory. Applications of Diophantine approximation to these problems will be given and will include a connection with LISA (Laser Interferometer Space Antenna), a space-based gravity wave detector under construction.
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Finite Geometries: Classical Problems and Recent Developments 15:10 Fri 20 Jul 07 | G04, Napier Building, University of Adelaide | Prof. Joseph A. Thas | Ghent University, Belgium
Abstract...In recent years there has been an increasing interest in finite projective spaces, and important applications to practical topics such as coding theory, cryptography and design of experiments have made the field even more attractive. In my talk some classical problems and recent developments will be discussed. First I will mention Segre's celebrated theorem and ovals and a purely combinatorial characterization of Hermitian curves in the projective plane over a finite field here, from the beginning, the considered pointset is contained in the projective plane over a finite field. Next, a recent elegant result on semiovals in PG(2,q), due to Gács, will be given. A second approach is where the object is described as an incidence structure satisfying certain properties; here the geometry is not a priori embedded in a projective space. This will be illustrated by a characterization of the classical inversive plane in the odd case. Another quite recent beautiful result in Galois geometry is the discovery of an infinite class of hemisystems of the Hermitian variety in PG(3,q^2), leading to new interesting classes of incidence structures, graphs and codes; before this result, just one example for GF(9), due to Segre, was known.
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The Linear Algebra of Internet Search Engines 15:10 Fri 5 Oct 07 | G04, Napier Building, University of Adelaide | Dr Lesley Ward | School of Mathematics and Statistics, University of South Australia
Abstract...We often want to search the web for information on a given topic. Early web-search algorithms worked by counting up the number of times the words in a query topic appeared on each webpage. If the topic words appeared often on a given page, that page was ranked highly as a source of information on that topic.
More recent algorithms rely on Link Analysis. People make judgments about how useful a given page is for a given topic, and they express these judgments through the hyperlinks they choose to put on their own webpages. Link-analysis algorithms aim to mine the collective wisdom encoded in the resulting network of links.
I will discuss the linear algebra that forms the common underpinning of three link-analysis algorithms for web search. I will also present some work on refining one such algorithm, Kleinberg's HITS algorithm.
This is joint work with Joel Miller, Greg Rae, Fred Schaefer, Ayman Farahat, Tom LoFaro, Tracy Powell, Estelle Basor, and Kent Morrison. It originated in a Mathematics Clinic project at Harvey Mudd College.
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Add one part chaos, one part topology, and stir well... 13:10 Fri 19 Oct 07 | Engineering North 132 | Dr Matt Finn
Abstract...Stirring and mixing of fluids occurs everywhere, from adding milk to a cup of coffee, right through to industrial-scale chemical blending. So why stir in the first place? Is it possible to do it badly? And how can you make sure you do it effectively? I will attempt to answer these questions using a few thought experiments, some dynamical systems theory and a little topology.
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Groundwater: using mathematics to solve our water crisis 13:10 Wed 9 Apr 08 | Napier 210 | Dr Michael Teubner
Abstract...'The driest state in the driest continent' is how South
Australia used to be described. And that was before the drought! Now
we have severe water restrictions, dead lawns, and dying gardens.
But this need not be the case. Mathematics to the rescue!
Groundwater exists below much of the Adelaide metro area. We can
store winter stormwater in the ground and use it when we need it in
summer. But we need mathematical models to understand where
groundwater exists, where we can inject stormwater and how much
can be stored, and where we can extract it: all through mathematical
models. Come along and see that we don't have a water problem, we
have a water management problem.
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Global and Local stationary modelling in finance: Theory and empirical evidence 14:10 Thu 10 Apr 08 | G04, Napier Building, University of Adelaide | Prof. Dominique Guégan | Universite Paris 1 Pantheon-Sorbonne
Abstract...To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guégan, 1994), the EXPAR model (Haggan and Ozaki, 1980), the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guégan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under specific conditions on the parameters, then the forecast points and the forecast intervals are available.
Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense.
Now non-stationarity modelling has also a long tradition in econometrics. This one is based on the conditional moments of the data generating process. It appears mainly in the heteroscedastic and volatility models, like the GARCH and related models, and stochastic volatility processes (Ghysels, Harvey and Renault 1997). This non-stationarity appears also in a different way with structural changes models like the switching models (Hamilton, 1988), the stopbreak model (Diebold and Inoue, 2001, Breidt and Hsu, 2002, Granger and Hyung, 2004) and the SETAR models, for instance. It can also be observed from linear models with time varying coefficients (Nicholls and Quinn, 1982, Tsay, 1987).
Thus, using stationary unconditional moments suggest a global stationarity for the model, but using non-stationary unconditional moments or non-stationary conditional moments or assuming existence of states suggest that this global stationarity fails and that we only observe a local stationary behavior.
The growing evidence of instability in the stochastic behavior of stocks, of exchange rates, of some economic data sets like growth rates for instance, characterized by existence of volatility or existence of jumps in the variance or on the levels of the prices imposes to discuss the assumption of global stationarity and its consequence in modelling, particularly in forecasting. Thus we can address several questions with respect to these remarks.
1. What kinds of non-stationarity affect the major financial and economic data sets? How to detect them?
2. Local and global stationarities: How are they defined?
3. What is the impact of evidence of non-stationarity on the statistics computed from the global non stationary data sets?
4. How can we analyze data sets in the non-stationary global framework? Does the asymptotic theory work in non-stationary framework?
5. What kind of models create local stationarity instead of global stationarity? How can we use them to develop a modelling and a forecasting strategy?
These questions began to be discussed in some papers in the economic literature. For some of these questions, the answers are known, for others, very few works exist. In this talk I will discuss all these problems and will propose 2 new stategies and modelling to solve them. Several interesting topics in empirical finance awaiting future research will also be discussed.
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The Mathematics of String Theory 15:10 Fri 2 May 08 | LG29, Napier Building, University of Adelaide | Prof. Peter Bouwknegt | Department of Mathematics, ANU
Abstract...String Theory has had, and continues to have, a profound impact on
many areas of mathematics and vice versa. In this talk I want to
address some relatively recent developments. In particular I will
argue, following Witten and others, that D-brane charges take values
in the K-theory of spacetime, rather than in integral cohomology as
one might have expected. I will also explore the mathematical
consequences of a particular symmetry, called T-duality, in this context.
I will give an intuitive introduction into D-branes and K-theory.
No prior knowledge about either String Theory, D-branes or K-theory
is required.
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The limits of proof 13:10 Wed 21 May 08 | Napier 210 | A/Prof Finnur Larusson
Abstract...The job of the mathematician is to discover new
truths about mathematical objects and their relationships.
Such truths are established by proving them. This raises a
fundamental question. Can every mathematical truth be
proved (by a sufficiently clever being) or are there truths
that will forever lie beyond the reach of proof?
Mathematics can be turned on itself to investigate this
question. In this talk, we will see that under certain
assumptions about proofs, there are truths that cannot be
proved. You must decide for yourself whether you think
these assumptions are valid!
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Puzzle-based learning: Introduction to mathematics 15:10 Fri 23 May 08 | LG29, Napier Building, University of Adelaide | Prof. Zbigniew Michalewicz | School of Computer Science, University of Adelaide
Abstract...The talk addresses a gap in the educational curriculum for 1st year students by proposing a new course that aims at getting students to think about how to frame and solve unstructured problems. The idea is to increase the student's mathematical awareness and problem-solving skills by discussing a variety of puzzles. The talk makes an argument that this approach - called Puzzle-Based Learning - is very beneficial for introducing mathematics, critical thinking, and problem-solving skills.
The new course has been approved by the University of Adelaide for Faculty of Engineering, Computer Science, and Mathematics. Many other universities are in the process of introducing such a course. The course will be offered in two versions: (a) full-semester course and (b) a unit within general course (e.g. Introduction to Engineering). All teaching materials (power point slides, assignments, etc.) are being prepared. The new textbook (Puzzle-Based Learning: Introduction to Critical Thinking, Mathematics, and Problem Solving) will be available from June 2008. The talk provides additional information on this development.
For further information see http://www.PuzzleBasedlearning.edu.au/
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Betti's Reciprocal Theorem for Inclusion and Contact Problems 15:10 Fri 1 Aug 08 | G03, Napier Building, University of Adelaide | Prof. Patrick Selvadurai | Department of Civil Engineering and Applied Mechanics, McGill University
Abstract...Enrico Betti (1823-1892) is recognized in the mathematics community for his pioneering contributions to topology. An equally important contribution is his formulation of the reciprocity theorem applicable to elastic bodies that satisfy the classical equations of linear elasticity. Although James Clerk Maxwell (1831-1879) proposed a law of reciprocal displacements and rotations in 1864, the contribution of Betti is acknowledged for its underlying formal mathematical basis and generality. The purpose of this lecture is to illustrate how Betti's reciprocal theorem can be used to full advantage to develop compact analytical results for certain contact and inclusion problems in the classical theory of elasticity. Inclusion problems are encountered in number of areas in applied mechanics ranging from composite materials to geomechanics. In composite materials, the inclusion represents an inhomogeneity that is introduced to increase either the strength or the deformability characteristics of resulting material. In geomechanics, the inclusion represents a constructed material region, such as a ground anchor, that is introduced to provide load transfer from structural systems. Similarly, contact problems have applications to the modelling of the behaviour of indentors used in materials testing to the study of foundations used to distribute loads transmitted from structures. In the study of conventional problems the inclusions and the contact regions are directly loaded and this makes their analysis quite straightforward. When the interaction is induced by loads that are placed exterior to the indentor or inclusion, the direct analysis of the problem becomes inordinately complicated both in terns of formulation of the integral equations and their numerical solution. It is shown by a set of selected examples that the application of Betti's reciprocal theorem leads to the development of exact closed form solutions to what would otherwise be approximate solutions achievable only through the numerical solution of a set of coupled integral equations.
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Elliptic equation for diffusion-advection flows 15:10 Fri 15 Aug 08 | G03, Napier Building, University of Adelaide | Prof. Pavel Bedrikovsetsky | Australian School of Petroleum Science, University of Adelaide.
Abstract...
The standard diffusion equation is obtained by Einstein's method and its generalisation, Fokker-Plank-Kolmogorov-Feller theory. The time between jumps in Einstein derivation is constant.
We discuss random walks with residence time distribution, which occurs for flows of solutes and suspensions/colloids in porous media, CO2 sequestration in coal mines, several processes in chemical, petroleum and environmental engineering. The rigorous application of the Einstein's method results in new equation, containing the time and the mixed dispersion terms expressing the dispersion of the particle time steps.
Usually, adding the second time derivative results in additional initial data. For the equation derived, the condition of limited solution when time tends to infinity provides with uniqueness of the Caushy problem solution.
The solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions of the direct simulation.
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Symmetry-breaking and the Origin of Species 15:10 Fri 24 Oct 08 | G03, Napier Building, University of Adelaide | Toby Elmhirst | ARC Centre of Excellence for Coral Reef Studies, James Cook University
Abstract...The theory of partial differential equations can say much about generic bifurcations from spatially homogeneous steady states, but relatively little about generic bifurcations from unimodal steady states. In many applications, spatially homogeneous steady states correspond to low-energy physical states that are destabilized as energy is fed into the system, and in these cases standard PDE theory can yield some impressive and elegant results. However, for many macroscopic biological systems such results are less useful because low-energy states do not hold the same priviledged position as they do in physical and chemical systems. For example, speciation -- the evolutionary process by which new species are formed -- can be seen as the destabilization of a unimodal density distribution over phenotype space. Given the diversity of species and environments, generic results are clearly needed, but cannot be gained from PDE theory. Indeed, such questions cannot even be adequately formulated in terms of PDEs. In this talk I will introduce 'Pod Systems' which can provide an answer to the question; 'What happens, generically, when a unimodal steady state loses stability?' In the pod system formalization, the answer involves elements of equivariant bifurcation theory and suggests that new species can arise as the result of broken symmetries.
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On the Henstock-Kurzweil integral (along with concerns about general math education in Europe) 15:10 Fri 13 Feb 09 | Napier LG28 | Professor Jean-Pierre Demailly | University of Grenoble, France
Abstract...The talk will be the occasion to take a few minutes to describe the situation of math education in France and in Europe, to motivate the interest of the lecturer in trying to bring back rigorous proofs in integration theory. The remaining 45 minutes will be devoted to explaining the basics of Henstock-Kurzweil integration theory, which, although not a response to education problems, is a modern and elementary approach of a very strong extension of the Riemann integral, providing easy access to several fundamental results of Lebesgue theory (monotone convergence theorem, existence of Lebesgue measure, etc.).
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String structures and characteristic classes for loop group bundles 13:10 Fri 1 May 09 | School Board Room | Mr Raymond Vozzo | University of Adelaide
Abstract...The Chern-Weil homomorphism gives a geometric method for calculating characteristic classes for principal bundles. In infinite dimensions, however, the standard theory fails due to analytical problems. In this talk I shall give a geometric method for calculating characteristic classes for principal bundle with structure group the loop group of a compact group which side-steps these complications. This theory is inspired in some sense by results on the string class (a certain cohomology class on the base of a loop group bundle) which I shall outline.
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Nonlinear diffusion-driven flow in a stratified viscous fluid 15:00 Fri 26 Jun 09 | Macbeth Lecture Theatre | Associate Professor Michael Page | Monash University
Abstract...In 1970, two independent studies (by Wunsch and Phillips) of the behaviour of a linear density-stratified viscous fluid in a closed container demonstrated a slow flow can be generated simply due to the container having a sloping boundary surface This remarkable motion is generated as a result of the curvature of the lines of constant density near any sloping surface, which in turn enables a zero normal-flux condition on the density to be satisfied along that boundary. When the Rayleigh number is large (or equivalently Wunsch's parameter $R$ is small) this motion is concentrated in the near vicinity of the sloping surface, in a thin `buoyancy layer' that has many similarities to an Ekman layer in a rotating fluid.
A number of studies have since considered the consequences of this type of `diffusively-driven' flow in a semi-infinite domain, including in the deep ocean and with turbulent effects included. More recently, Page & Johnson (2008) described a steady linear theory for the broader-scale mass recirculation in a closed container and demonstrated that, unlike in previous studies, it is possible for the buoyancy layer to entrain fluid from that recirculation. That work has since been extended (Page & Johnson, 2009) to the nonlinear regime of the problem and some of the similarities to and differences from the linear case will be described in this talk. Simple and elegant analytical solutions in the limit as $R \to 0$ still exist in some situations, and they will be compared with numerical simulations in a tilted square container at small values of $R$. Further work on both the unsteady flow properties and the flow for other geometrical configurations will also be described.
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Weak Hopf algebras and Frobenius algebras 13:10 Fri 21 Aug 09 | School Board Room | Prof Ross Street | Macquarie University
Abstract...A basic example of a Hopf algebra is a group algebra: it is the vector space having the group as basis and having multiplication linearly extending that of the group. We can start with a category instead of a group, form the free vector space on the set of its morphisms, and define multiplication to be composition when possible and zero when not. The multiplication has an identity if the category has finitely many objects; this is a basic example of a weak bialgebra. It is a weak Hopf algebra when the category is a groupoid. Group algebras are also Frobenius algebras. We shall generalize weak bialgebras and Frobenius algebras to the context of monoidal categories and describe some of their theory using the geometry of string diagrams.
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From linear algebra to knot theory 15:10 Fri 21 Aug 09 | Badger Labs G13
Macbeth Lecture Theatre | Professor Ross Street | Macquarie University, Sydney
Abstract...Vector spaces and linear functions form our paradigmatic monoidal category. The concepts underpinning linear algebra admit definitions, operations and constructions with analogues in many other parts of mathematics. We shall see how to generalize much of linear algebra to the context of monoidal categories. Traditional examples of such categories are obtained by replacing vector spaces by linear representations of a given compact group or by sheaves of vector spaces. More recent examples come from low-dimensional topology, in particular, from knot theory where the linear functions are replaced by braids or tangles. These geometric monoidal categories are often free in an appropriate sense, a fact that can be used to obtain algebraic invariants for manifolds.
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Defect formulae for integrals of pseudodifferential symbols:
applications to dimensional regularisation and index theory 13:10 Fri 4 Sep 09 | School Board Room | Prof Sylvie Paycha | Universite Blaise Pascal, Clermont-Ferrand, France
Abstract...The ordinary integral on L^1 functions on R^d unfortunately does not
extend to a translation invariant linear form on the whole algebra of
pseudodifferential symbols on R^d, forcing to work with ordinary linear
extensions which fail to be translation invariant. Defect formulae which express the difference between various linear extensions, show that they differ by local terms involving the noncommutative residue. In particular, we shall show how integrals regularised by a "dimensional regularisation" procedure familiar to physicists differ from Hadamard finite part (or "cut-off" regularised) integrals by a residue. When extended to pseudodifferential operators on closed manifolds, these defect formulae express the zeta regularised traces of a differential
operator in terms of a residue of its logarithm. In particular, we shall express the index of a Dirac type operator on a closed manifold in
terms of a logarithm of a generalized Laplacian, thus giving an a priori local
description of the index and shall discuss further applications.
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Curved pipe flow and its stability 15:10 Fri 11 Sep 09 | Badger labs G13
Macbeth Lecture Theatre | Dr Richard Clarke | University of Auckland
Abstract...The unsteady flow of a viscous fluid through a curved pipe is a widely occuring and well studied problem. The stability of such flows, however, has largely been overlooked; this is in marked contrast to flow through a straight-pipe, examination of which forms a cornerstone of hydrodynamic stability theory. Importantly, however, flow through a curved pipe exhibits an array of flow structures that are simply not present in the zero curvature limit, and it is natural to expect these to substantially impact upon the flow's stability. By considering two very different kinds of flows through a curved pipe, we illustrate that this can indeed be the case.
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Statistical Analysis for Harmonized Development of Systemic Organs in Human Fetuses 11:00 Thu 17 Sep 09 | School Board Room | Professor Kanta Naito | Shimane University, Japan
Abstract...The growth processes of human babies have been studied
sufficiently in scientific fields, but there have still been many issues
about the developments of human fetus which are not clarified. The aim of
this research is to investigate the developing process of systemic organs of
human fetuses based on the data set of measurements of fetus's bodies and
organs. Specifically, this talk is concerned with giving a mathematical
understanding for the harmonized developments of the organs of human
fetuses. The method to evaluate such harmonies is proposed by the use of the
maximal dilatation appeared in the theory of quasi-conformal mapping.
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Understanding hypersurfaces through tropical geometry 12:10 Fri 25 Sep 09 | Napier 102 | Dr Mohammed Abouzaid | Massachusetts Institute of Technology
Abstract...Given a polynomial in two or more variables, one may study the
zero locus from the point of view of different mathematical subjects
(number theory, algebraic geometry, ...). I will explain how tropical
geometry allows to encode all topological aspects by elementary
combinatorial objects called "tropical varieties."
Mohammed Abouzaid received a B.S. in 2002 from the University of Richmond, and a Ph.D. in 2007 from the University of Chicago under the supervision of Paul Seidel. He is interested in symplectic topology and its interactions with algebraic geometry and differential topology, in particular the homological mirror symmetry conjecture. Since 2007 he has been a postdoctoral fellow at MIT, and a Clay Mathematics Institute Research Fellow.
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Stable commutator length 13:40 Fri 25 Sep 09 | Napier 102 | Professor Danny Calegari | California Institute of Technology
Abstract...Stable commutator length answers the question: "what is the simplest
surface in a given space with prescribed boundary?" where "simplest"
is interpreted in topological terms. This topological definition is
complemented by several equivalent definitions - in group theory, as a
measure of non-commutativity of a group; and in linear programming, as
the solution of a certain linear optimization problem. On the
topological side, scl is concerned with questions such as computing
the genus of a knot, or finding the simplest 4-manifold that bounds a
given 3-manifold. On the linear programming side, scl is measured in
terms of certain functions called quasimorphisms, which arise from
hyperbolic geometry (negative curvature) and symplectic geometry
(causal structures). In these talks we will discuss how scl in free
and surface groups is connected to such diverse phenomena as the
existence of closed surface subgroups in graphs of groups, rigidity
and discreteness of symplectic representations, bounding immersed
curves on a surface by immersed subsurfaces, and the theory of multi-
dimensional continued fractions and Klein polyhedra.
Danny Calegari is the Richard Merkin Professor of Mathematics at the California Institute of Technology, and is one of the recipients of the 2009 Clay Research Award for his work in geometric topology and geometric group theory. He received a B.A. in 1994 from the University of Melbourne, and a Ph.D. in 2000 from the University of California, Berkeley under the joint supervision of Andrew Casson and William Thurston. From 2000 to 2002 he was Benjamin Peirce Assistant Professor at Harvard University, after which he joined the Caltech faculty; he became Richard Merkin Professor in 2007.
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The proof of the Poincare conjecture 15:10 Fri 25 Sep 09 | Napier 102 | Professor Terrence Tao | UCLA
Abstract...In a series of three papers from 2002-2003, Grigori Perelman gave a spectacular proof of the Poincare Conjecture (every smooth compact simply connected three-dimensional manifold is topologically isomorphic to a sphere), one of the most famous open problems in mathematics (and one of the seven Clay Millennium Prize Problems worth a million dollars each), by developing several new groundbreaking advances in Hamilton's theory of Ricci flow on manifolds. In this talk I describe in broad detail how the proof proceeds, and briefly discuss some of the key turning points in the argument.
About the speaker:
Terence Tao was born in Adelaide, Australia, in 1975. He has been a professor of mathematics at UCLA since 1999, having completed his PhD under Elias Stein at Princeton in 1996. Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory. He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal and SASTRA Ramanujan Prize in 2006, and the MacArthur Fellowship and Ostrowski Prize in 2007. Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society and the Australian Academy of Sciences (Corresponding Member).
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Is the price really right? 12:10 Thu 22 Oct 09 | Napier 210 | Mr Sam Cohen | University of Adelaide
Abstract...Making decisions when outcomes are uncertain is a common problem we all face. In this talk I will outline some recent developments on this question from the mathematics of finance-the theory of risk measures and nonlinear expectations. I will also talk about how decisions are currently made in the finance industry, and how some simple mathematics can show where these systems are open to abuse.
Media for this event...
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ANZIAM Conference 00:00 Sun 31 Jan 10 | Queenstown, New Zealand
Abstract...ANZIAM is a division of the Australian Mathematical Society. It is the professional association for industrial and applied mathematics in Australia and New Zealand. The annual conference of ANZIAM is an established gathering of applied mathematicians, scientists and engineers. In 2010 the venue is Rydges Hotel, Queenstown, New Zealand.
Media for this event...
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News matching "Mathematics of string theory"
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Usenet Conference Associate Professor Matt Roughan (Applied Mathematics) has been invited to Co-Chair the Association for Computing Machinery Usenet Internet Measurement Conference. Posted Mon 15 Jan 07.
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Dr Yvonne Stokes wins Michell Medal Dr Yvonne Stokes (Applied Mathematics) was awarded the 2007 J.H. Michell Medal of ANZIAM. The award is made annually to an outstanding new researcher, one who is in the first ten years of their research career. Read Yvonne's citation here. Posted Mon 5 Mar 07.
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ARC success The School of Mathematical Sciences was again very successful in attracting Australian Research Council funding for 2008. Recipients of ARC Discovery Projects are (with staff from the School highlighted):
Prof NG Bean; Prof PG Howlett; Prof CE Pearce; Prof SC Beecham; Dr AV Metcalfe; Dr JW Boland:
WaterLog - A mathematical model to implement recommendations of The Wentworth Group.
2008-2010: $645,000
Prof RJ Elliott:
Dynamic risk measures.
(Australian Professorial Fellowship)
2008-2012: $897,000
Dr MD Finn:
Topological Optimisation of Fluid Mixing.
2008-2010: $249,000
Prof PG Bouwknegt; Prof M Varghese; A/Prof S Wu:
Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program.
2008-2010: $240,000
The latter grant is held through the ANU Posted Wed 26 Sep 07.
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Mathematics Building to be demolished The existing mathematics building will be demolished to make way for a new 8-storey, 6-star building. The new building, which is expected to be completed for the start of semester 1, 2010, will house the Schools of Electrical and Electronic Engineering, Computer Science and Mathematical Sciences. The demolition will begin on 10th December 2007. See the Building Life Impact web-site for more details. Posted Mon 12 Nov 07.
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School to move to new accommodation In anticipation of the demolition of the existing Mathematics building, the School of Mathematical Sciences will be moving to new temporary accommodation. As from 10th December 2007 we can be found on level 3 (School Office) and 4 of 10 Pulteney Street. Posted Mon 10 Dec 07.
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Potts Medal Winner Professor Charles Pearce, the Elder Profesor of Mathematics, was awarded the Ren Potts Medal by the Australian Society for Operations
Research at its annual meeting in December. This is a national award for outstanding
contributions to Operations Research in Australia.
Posted Tue 22 Jan 08.
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University Implementation Grant for Learning and Teaching Enhancements Congratulations to Dr Adrian Koerber and Dr Paul McCann who have been successful in securing $40,000 funding from
the University Implementation Grant for Learning and Teaching Enhancements. Their proposal "An enhanced implementation of Maple T.A.
in mathematics service courses" will expand the use of Maple TA, and online assessment, further into the School large second year
service courses. Posted Fri 18 Apr 08.
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Open Day Innovation Fund Success Congratulations to Associate Professor Matt Roughan, Mr David Butler and Mr Jono Tuke who have been awarded
$2000 from the Open Day Innovation Fund for their project "Tactile Mathematics". Posted Fri 18 Apr 08.
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Positions available in the School (5) The School is currently seeking a Professor of Statistics, an Associate Professor of Statistics, a Lecturer/Senior Lecturer in Applied Mathematics, a Lecturer in Applied Mathematics and a Lecturer in Pure Mathematics. See the University's jobs website for full details, including the selection criteria. Posted Fri 23 May 08.
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Teaching Fellow Position Visiting Teaching Fellow School of Mathematical Sciences (Ref: 3808)
We are seeking a Visiting Teaching Fellow (Associate Lecturer) who will be
responsible for developing better links between the University of Adelaide
and secondary schools and developing new approaches for first-year
undergraduate teaching. You will be required to conduct tutorials in first
year mathematics and statistics subjects for up to 16 hours per week, and
assist in subject assessment and curriculum development.
This position would suit an experienced mathematics teacher with strong
mathematical training and an interest and recent involvement in teaching
advanced mathematics units in years 11 and 12. Fixed-term position available
from 19 January 2009 to 31 December 2009. Salary: (Level A) $49,053 -
$66,567 per annum.Plus an employer superannuation contribution of 17%
applies. (Closing date 14/11/08.)
Please see the University web site for further details. Posted Wed 17 Sep 08.
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Sam Cohen wins prize for best student talk at ANZIAM 2009 Congratulations to Mr Sam Cohen, a PhD student within the School, who was awarded the T. M. Cherry Prize for the best student paper at the 2009 meeting of ANZIAM for his talk on
A general theory of backward stochastic difference equations. Posted Fri 6 Feb 09.
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Positions available in the School (2) The School expects to advertise two tenurable ("tenure track") positions, one in Pure Mathematics and one in Applied Mathematics, in the coming month. Please check back regularly for further details. Posted Fri 6 Mar 09.
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Mini Winter School on Geometry and Physics The Institute for Geometry and its Applications will host a Winter School on Geometry and Physics on 20-22 July 2009. There will be three days of expository lectures aimed at 3rd year and honours students interested in postgraduate studies in pure mathematics or mathematical physics. Posted Wed 24 Jun 09.More information...
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Position available: Lecturer in Applied Mathematics The School is currently seeking to appoint a Lecturer in Applied Mathematics in the area of optimisation. See the University's jobs website for full details, including the selection criteria. Posted Wed 26 Aug 09.
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Position available: Professor of Pure Mathematics The School is currently seeking to appoint a Professor of Pure Mathematics. See the University's jobs website for full details, including the selection criteria. Posted Fri 18 Sep 09.More information...
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ARC Grant successes Congratulations to Tony Roberts, Charles Pearce, Robert Elliot, Andrew Metcalfe and all their collaborators on their success in the current round of ARC grants. The projects are "Development of innovative technologies for oil production based on the advanced theory of suspension flows in porous media" (Tony Roberts et al.), "Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems" (Charles Pearce et al.),
"Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models" (Robert Elliott et al.) and "A new flood design methodology for a variable and changing climate" (Andrew Metcalfe et al.) Posted Mon 26 Oct 09.
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Publications matching "Mathematics of string theory"
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Non-commutative correspondences, duality and D-branes in bivariant K-theory
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Advances in Theoretical and Mathematical Physics 13 (497–552) 2009 |
Portfolio risk minimization and differential games
Elliott, Robert; Siu, T, Nonlinear Analysis-Theory Methods & Applications In Press (–) 2009 |
The decay of suddenly blocked flow in a curved pipe
Clarke, Robert; Denier, James, Journal of Engineering Mathematics 63 (241–257) 2009 |
The maximum size of the intersection of two ovoids
Butler, David, Journal of Combinatorial Theory Series A 116 (242–245) 2009 |
Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field
Ikbal, M; Chakravarty, S; Wong, Kelvin; Mazumdar, Jagan; Mandal, P, Journal of Computational and Applied Mathematics 230 (243–259) 2009 |
Elementary Calculus of Financial Mathematics
Roberts, Anthony John, (Society for Industrial and Applied Mathematics) 2009 |
D-branes, KK-theory and duality on noncommutative spaces
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Journal of Physics: Conference Series (Print Edition) 103 (1–13) 2008 |
Holomorphic classification of four-dimensional surfaces in C3
Beloshapka, V; Ezhov, Vladimir; Schmalz, G, Izvestiya Mathematics 72 (413–427) 2008 |
Influence of rapid changes in a channel bottom on free-surface flows
Binder, Benjamin; Dias, F; Vanden-Broeck, J, IMA Journal of Applied Mathematics 73 (254–273) 2008 |
Some U-Statistics in goodness-of-fit tests derived from characterizations via record values
Morris, Kerwin; Szynal, D, International Journal of Pure and Applied Mathematics 46 (507–582) 2008 |
Synchronization of neural networks based on parameter identification and via output or state coupling
Lou, X; Cui, B, Journal of Computational and Applied Mathematics 222 (440–457) 2008 |
The mathematical modelling of rotating capillary tubes for holey-fibre manufacture
Voyce, Christopher; Fitt, A; Monro, Tanya, Journal of Engineering Mathematics 60 (69–87) 2008 |
Using distortions of copulas to price synthetic CDOs
Crane, Glenis Jayne; Van Der Hoek, John, Insurance Mathematics & Economics 42 (903–908) 2008 |
Thomas P. Branson (1953?2006) - Professor of Mathematics, University of Iowa
Chang, A; Eastwood, Michael; Gover, R; Jorgensen, P; Olafsson, G; Oersted, B; Yang, P; Peterson, L; Svidersky, O; Ugalde, W; Hong, P, Acta Applicandae Mathematicae 102 (127–129) 2008 |
Aspects of Dirac operators in analysis
Eastwood, Michael; Ryan, J, Milan Journal of Mathematics 75 (91–116) 2007 |
Computation of extensional fall of slender viscous drops by a one-dimensional eulerian method
Hajek, Bronwyn; Stokes, Yvonne; Tuck, Ernest, Siam Journal on Applied Mathematics 67 (1166–1182) 2007 |
Goodness-of-fit tests based on characterizations involving moments of order statistics
Morris, Kerwin; Szynal, D, International Journal of Pure and Applied Mathematics 38 (83–121) 2007 |
Nonclassical symmetry solutions for reaction-diffusion equations with explicity spatial dependence
Hajek, Bronwyn; Edwards, M; Broadbridge, P; Williams, G, Nonlinear Analysis-Theory Methods & Applications 67 (2541–2552) 2007 |
Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras
Eastwood, Michael; Somberg, P; Soucek, V, Journal of Geometry and Physics 57 (2539–2546) 2007 |
T-Duality in type II string theory via noncommutative geometry and beyond
Varghese, Mathai, Progress of Theoretical Physics Supplement 171 (237–257) 2007 |
The twistor construction and Penrose transform in split signature
Eastwood, Michael, The Asian Journal of Mathematics 11 (103–111) 2007 |
A biography of J. N. Newman
Tuck, Ernest, Journal of Engineering Mathematics 58 (1–5) 2007 |
Cayley hypersurfaces
Eastwood, Michael; Ezhov, Vladimir, Steklov Institute of Mathematics. Proceedings 253 (221–224) 2006 |
Duality symmetry and the form fields of M-theory
Sati, Hicham, The Journal of High Energy Physics (Print Edition) 6 (0–10) 2006 |
Dynamic portfolio allocation, the dual theory of choice and probability distortion functions
Hamada, M; Sherris, M; Van Der Hoek, John, Astin Bulletin 31 (187–217) 2006 |
Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q)
Barwick, Susan; Brown, Matthew; Penttila, T, Journal of Combinatorial Theory Series A 113 (273–290) 2006 |
Heat kernels and the range of the trace on completions of twisted group algebras
Varghese, Mathai, Contemporary Mathematics 398 (321–345) 2006 |
Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians
Dodziuk, Josef; Varghese, Mathai, Contemporary Mathematics 398 (69–82) 2006 |
Linear transformations on codes
Glynn, David; Gulliver, T; Gupta, M, Discrete Mathematics 306 (1871–1880) 2006 |
On a generalised Connes-Hochschild-Kostant-Rosenberg theorem
Varghese, Mathai; Stevenson, Daniel, Advances in Mathematics 200 (303–335) 2006 |
Prolongations of geometric overdetermined systems
Branson, T; Cap, A; Eastwood, Michael; Gover, A, International Journal of Mathematics 17 (641–664) 2006 |
Some Penrose transforms in complex differential geometry
Anco, S; Bland, J; Eastwood, Michael, Science in China Series A-Mathematics Physics Astronomy 49 (1599–1610) 2006 |
The elliptic curves in gauge theory, string theory, and cohomology
Sati, Hicham, The Journal of High Energy Physics (Print Edition) 3 (0–19) 2006 |
The instability of the flow in a suddenly blocked pipe
Jewell, Nathaniel; Denier, James, Quarterly Journal of Mechanics and Applied Mathematics 59 (651–673) 2006 |
Yang-Mills theory for bundle gerbes
Varghese, Mathai; Roberts, David, Journal of Physics A: Mathematical and Theoretical (Print Edition) 39 (6039–6044) 2006 |
K-theory
Varghese, Mathai, chapter in Encyclopedia of mathematical physics (Elsevier Academic Press) 246–254, 2006 |
Resolving the multitude of microscale interactions accurately models stochastic partial differential equations
Roberts, Anthony John, London Mathematical Society. Journal of Computation and Mathematics 9 (193–221) 2006 |
Class-D audio amplifiers with negative feedback
Cox, Stephen; Candy, B, Siam Journal on Applied Mathematics 66 (468–488) 2005 |
Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory
Kordyukov, Y; Varghese, Mathai; Shubin, M, Journal fur die Reine und Angewandte Mathematik 581 (193–236) 2005 |
Examples of unbounded homogeneous domains in complex space
Eastwood, Michael; Isaev, A, Science in China Series A-Mathematics Physics Astronomy 48 (248–261) 2005 |
Generalized quadrangles and regularity
Brown, Matthew, Discrete Mathematics 294 (25–42) 2005 |
Goodness-of-fit tests via characterizations
Morris, Kerwin; Szynal, D, International Journal of Pure and Applied Mathematics 23 (491–555) 2005 |
Hamiltonian dynamics and morse topology of humanoid robots
Ivancevic, V; Pearce, Charles, Global Journal of Mathematics and Mathematical Sciences (GJMMS) 1 (9–19) 2005 |
Higher symmetries of the Laplacian
Eastwood, Michael, Annals of Mathematics 161 (1645–1665) 2005 |
L2 torsion without the determinant class condition and extended L2 cohomology
Braverman, M; Carey, Alan; Farber, M; Varghese, Mathai, Communications in Contemporary Mathematics 7 (421–462) 2005 |
M-theory and characteristic classes
Sati, Hicham, The Journal of High Energy Physics (Online Editions) 8 (020-1–020-8) 2005 |
On some polynomial-like inequalities of Brenner and Alzer
Pearce, Charles; Pecaric, Josip, Journal of Inequalities in Pure and Applied Mathematics 6 (WWW 1–WWW 5) 2005 |
Oriented site percolation, phase transitions and probability bounds
Pearce, Charles; Fletcher, F, Journal of Inequalities in Pure and Applied Mathematics 6 (WWW 1–WWW 15) 2005 |
Representations via overdetermined systems
Eastwood, Michael, Contemporary Mathematics 368 (201–210) 2005 |
Risk-sensitive filtering and smoothing for continuous-time Markov processes
Malcolm, William; Elliott, Robert; James, M, IEEE Transactions on Information Theory 51 (1731–1738) 2005 |
Self-similar "stagnation point" boundary layer flows with suction or injection
King, J; Cox, Stephen, Studies in Applied Mathematics 115 (73–107) 2005 |
Type II string theory and modularity
Kriz, I; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 8 (038-1–038-30) 2005 |
Type IIB string theory, S-duality, and generalized cohomology
Kriz, I; Sati, Hicham, Nuclear Physics B 715 (639–664) 2005 |
Updating the parameters of a threshold scheme by minimal broadcast
Barwick, Susan; Jackson, Wen-Ai; Martin, K, IEEE Transactions on Information Theory 51 (620–633) 2005 |
Free surface flows past surfboards and sluice gates
Binder, Benjamin; Vanden-Broeck, J, European Journal of Applied Mathematics 16 (601–619) 2005 |
Preface to the Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference, EMAC-2005
Stacey, A; Blyth, B; Shepherd, J; Roberts, Anthony John, The ANZIAM Journal 47 (–) 2005 |
Some Properties of the Capacity Value Function
Chiera, Belinda; Krzesinski, A; Taylor, Peter, Siam Journal on Applied Mathematics 65 (1407–1419) 2005 |
A deterministic discretisation-step upper bound for state estimation via Clark transformations
Malcolm, William; Elliott, Robert; Van Der Hoek, John, J.A.M.S.A. Journal of Applied Mathematics and Stochastic Analysis 2004 (371–384) 2004 |
A fundamental solution for linear second-order elliptic systems with variable coefficients
Clements, David, Journal of Engineering Mathematics 49 (209–216) 2004 |
A sufficient condition for the uniform exponential stability of time-varying systems with noise
Grammel, G; Maizurna, Isna, Nonlinear Analysis-Theory Methods & Applications 56 (951–960) 2004 |
Geometrical contributions to secret sharing theory
Jackson, Wen-Ai; Martin, K; O'Keefe, Christine, Journal of Geometry 79 (102–133) 2004 |
Kirillov theory for a class of discrete nilpotent groups
Tandra, Haryono; Moran, W, Canadian Journal of Mathematics-Journal Canadien de Mathematiques 56 (883–896) 2004 |
Large-Reynolds-number asymptotics of the Berman problem
Cox, Stephen; King, J, Studies in Applied Mathematics 113 (217–243) 2004 |
M-theory, type IIA superstrings, and elliptic cohomology
Kriz, I; Sati, Hicham, Advances in Theoretical and Mathematical Physics 8 (345–394) 2004 |
Mixing measures for a two-dimensional chaotic Stokes flow
Finn, Matthew; Cox, Stephen; Byrne, H, Journal of Engineering Mathematics 48 (129–155) 2004 |
Moduli of isolated hypersurface singularities
Eastwood, Michael, The Asian Journal of Mathematics 8 (305–314) 2004 |
Monads and bundles on rational surfaces
Buchdahl, Nicholas, Rocky Mountain Journal of Mathematics 34 (513–540) 2004 |
Pricing claims on non tradable assets
Elliott, Robert; Van Der Hoek, John, Contemporary Mathematics 351 (103–114) 2004 |
Some relations between twisted K-theory and E8 gauge theory
Varghese, Mathai; Sati, Hicham, The Journal of High Energy Physics (Online Editions) 3 (WWW 1–WWW 22) 2004 |
Subquadrangles of order s of generalized quadrangles of order (s, s2), Part I
Brown, Matthew; Thas, J, Journal of Combinatorial Theory Series A 106 (15–32) 2004 |
Subquadrangles of order s of generalized quadrangles of order (s, s2), Part II
Brown, Matthew; Thas, J, Journal of Combinatorial Theory Series A 106 (33–48) 2004 |
Mathematics of Financial Markets
Elliott, Robert; Kopp, P, (Springer) 2004 |
Measure Theory and Filtering: Introduction and Applications
Aggoun, L; Elliott, Robert, (Cambridge University Press) 2004 |
Arbitrage in a Discrete Version of the Wick-Fractional Black Scholes Model
Bender, C; Elliott, Robert, Mathematics of Operations Research 29 (935–945) 2004 |
Euler and his contribution to number theory
Glen, Amy; Scott, Paul, Australian Mathematics Teacher 1 (2–5) 2004 |
Some relations between twisted K-theory and E-8 gauge theory
Mathai, V; Sati, Hicham, The Journal of High Energy Physics (Online Editions) (WWW1–WWW22) 2004 |
Two-zone model of shear dispersion in a channel using centre manifolds
Roberts, Anthony John; Strunin, D, Quarterly Journal of Mechanics and Applied Mathematics 57 (363–378) 2004 |
A general fractional white noise theory and applications to finance
Elliott, Robert; Van Der Hoek, John, Mathematical Finance 13 (301–330) 2003 |
Approximating L2 invariants and the Atiyah conjecture
Dodziuk, Josef; Linnell, P; Varghese, Mathai; Schick, T; Yates, Stuart, Communications on Pure and Applied Mathematics 56 (839–873) 2003 |
Chern character in twisted K-theory: Equivariant and holomorphic cases
Varghese, Mathai; Stevenson, Daniel, Communications in Mathematical Physics 236 (161–186) 2003 |
Edge of the wedge theory in hypo-analytic manifolds
Eastwood, Michael; Graham, C, Communications in Partial Differential Equations 28 (2003–2028) 2003 |
Higgs fields, bundle gerbes and string structures
Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 243 (541–555) 2003 |
Interpolations of Jensen's inequality
Dragomir, S; Pearce, Charles; Pecaric, Josip, Tamkang Journal of Mathematics 34 (175–187) 2003 |
On some spectral results relating to the relative values of means
Pearce, Charles, Journal of Inequalities in Pure and Applied Mathematics 4 (1–7) 2003 |
Radon and Fourier transforms for D-modules
D'Agnolo, A; Eastwood, Michael, Advances in Mathematics 180 (452–485) 2003 |
The geometric triangle for 3-dimensional Seiberg-Witten monopoles
Carey, Alan; Marcolli, M; Wang, Bai-Ling, Communications in Contemporary Mathematics 5 (197–250) 2003 |
The nonparallel evolution of nonlinear short waves in buoyant boundary layers
Denier, James; Bassom, A, Studies in Applied Mathematics 110 (139–156) 2003 |
Type-1 D-branes in an H-flux and twisted KO-theory
Varghese, Mathai; Murray, Michael; Stevenson, Daniel, The Journal of High Energy Physics (Online Editions) 11 (www 1–www 22) 2003 |
A holistic finite difference approach models linear dynamics consistently
Roberts, Anthony John, Mathematics of Computation 72 (247–262) 2003 |
Modelling the dynamics of turbulent floods
Mei, Z; Roberts, Anthony John; Li, Z, Siam Journal on Applied Mathematics 63 (423–458) 2003 |
On a convexity problem arising in queueing theory and electromagnetism
Peake, M; Pearce, Charles, Sixth International Conference on Nonlinear Functional Analysis and Applications, Gyeongsang National University 01/09/00 |
A comparison of linear and nonlinear computations of waves made by slender submerged bodies
Tuck, Ernest; Scullen, David, Journal of Engineering Mathematics 42 (255–264) 2002 |
Axial anomaly and topological charge in lattice gauge theory with overlap dirac operator
Adams, Damian, Annals of Physics 296 (131–151) 2002 |
Families index theory for Overlap lattice Dirac operator. I
Adams, Damian, Nuclear Physics B 624 (469–484) 2002 |
Families index theory, gauge fixing, and topology of the space of lattice-gauge fields: a summary
Adams, Damian, Nuclear Physics B-Proceedings Supplements 109A (77–80) 2002 |
Inequalities for lattice constrained planar convex sets
Hillock, P; Scott, Paul, Journal of Inequalities in Pure and Applied Mathematics 3 (www 23:1–www 23:10) 2002 |
Ruled cubic surfaces in PG(4, q), Baer subplanes of PG(2, q2) and Hermitian curves
Casse, Rey; Quinn, Catherine, Discrete Mathematics 248 (17–25) 2002 |
Supporting maintenance strategies using Markov models
Al-Hassan, K; Swailes, D; Chan, J; Metcalfe, Andrew, IMA Journal of Management Mathematics 13 (17–27) 2002 |
The universal gerbe, Dixmier-Douady class, and gauge theory
Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 59 (47–60) 2002 |
Towards the inverse of a word
Clarke, Robert, Discrete Mathematics 256 (595–607) 2002 |
Twisted K-theory and K-theory of bundle gerbes
Bouwknegt, Pier; Carey, Alan; Varghese, Mathai; Murray, Michael; Stevenson, Daniel, Communications in Mathematical Physics 228 (17–45) 2002 |
Weak UCP and perturbed monopole equations
Booss-Bavnbek, B; Marcolli, M; Wang, Bai-Ling, International Journal of Mathematics 13 (987–1008) 2002 |
On an extremal problem arising in queueing theory and telecommunications
Peake, M; Pearce, Charles, chapter in Optimization and Related Topics (Kluwer Academic Publishers) 119–134, 2001 |
On positivity of the Kadison constant and noncommutative Bloch theory
Varghese, Mathai, The Fifth Pacific Rim Geometry Conference, Sendai, Japan 25/07/00 |
A class of non-expected utility risk measures and implications for asset allocations
Van Der Hoek, John; Sherris, M, Insurance Mathematics & Economics 28 (69–82) 2001 |
A classification of non-degenerate homogeneous equiaffine hypersurfaces in four complex dimensions
Eastwood, Michael; Ezhov, Vladimir, The Asian Journal of Mathematics 5 (721–740) 2001 |
Csiszr f-divergence, Ostrowski's inequality and mutual information
Dragomir, S; Gluscevic, Vido; Pearce, Charles, Nonlinear Analysis-Theory Methods & Applications 47 (2375–2386) 2001 |
Linearised cavity theory with smooth detachment
Haese, Peter, Australian Mathematical Society Gazette 28 (187–193) 2001 |
On Boutroux's tritronque solutions of the first Painlev equation
Joshi, Nalini; Kitaev, Alexandre, Studies in Applied Mathematics 107 (253–291) 2001 |
On Euler trapezoid formulae
Dedic, L; Matic, M; Pecaric, Josip, Applied Mathematics and Computation 123 (37–62) 2001 |
On the continuum limit of fermionic topological charge in lattice gauge theory
Adams, David, Journal of Mathematical Physics 42 (5522–5533) 2001 |
Plya-type inequalities for arbitrary functions
Pearce, Charles; Pecaric, Josip; Varosanec, S, Houston Journal of Mathematics 27 (601–612) 2001 |
Refinements of some bounds in information theory
Matic, M; Pearce, Charles; Pecaric, Josip, The ANZIAM Journal 42 (387–398) 2001 |
Some constructions of small generalized polygons
Polster, Burkhard; Van Maldeghem, H, Journal of Combinatorial Theory Series A 96 (162–179) 2001 |
Subquadrangles of generalized quadrangles of order (q2, q), q Even
O'Keefe, Christine; Penttila, T, Journal of Combinatorial Theory Series A 94 (218–229) 2001 |
The Mx/G/1 queue with queue length dependent service times
Choi, B; Kim, Y; Shin, Y; Pearce, Charles, J.A.M.S.A. Journal of Applied Mathematics and Stochastic Analysis 14 (399–419) 2001 |
The modelling and numerical simulation of causal non-linear systems
Howlett, P; Torokhti, Anatoli; Pearce, Charles, Nonlinear Analysis-Theory Methods & Applications 47 (5559–5572) 2001 |
Twisted index theory on good orbifolds, II: Fractional quantum numbers
Marcolli, M; Varghese, Mathai, Communications in Mathematical Physics 217 (55–87) 2001 |
Twistor results for integral transforms
Bailey, T; Eastwood, Michael, Contemporary Mathematics 278 (77–86) 2001 |
Introduction to Chern-Simons gauge theory on general 3-manifolds
Adams, David, chapter in Mathematical methods in physics (World Scientific Publishing) 1–43, 2000 |
Shannon's and related inequalities in information theory
Matic, M; Pearce, Charles; Pecaric, Josip, chapter in Survey on classical inequalities (Kluwer Academic Publishers) 127–164, 2000 |
Twistor theory
Murray, Michael, chapter in Geometric approaches to differential equations (Cambridge University Press) 201–223, 2000 |
A generalized trapezoid inequality for functions of bounded variation
Cerone, Pietro; Dragomir, S; Pearce, Charles, Turkish Journal of Mathematics 24 (147–163) 2000 |
A remark of Schwarz's topological field theory
Adams, David; Prodanov, E, Letters in Mathematical Physics 51 (249–255) 2000 |
Analytic continuation of vector bundles with Lp-curvature
Harris, A; Tonegawa, Y, International Journal of Mathematics 11 (29–40) 2000 |
Blowups and gauge fields
Buchdahl, Nicholas, Pacific Journal of Mathematics 196 (69–111) 2000 |
Bundle gerbes applied to quantum field theory
Carey, Alan; Mickelsson, J; Murray, Michael, Reviews in Mathematical Physics 12 (65–90) 2000 |
Bundle gerbes: stable isomorphism and local theory
Murray, Michael; Stevenson, Daniel, Journal of the London Mathematical Society 62 (925–937) 2000 |
CVBEM for a class of linear crack problems
Ang, W; Clements, David; Dehghan, M, Mathematics and Mechanics of Solids 4 (369–391) 2000 |
Correspondences, von Neumann algebras and holomorphic L2 torsion
Carey, Alan; Farber, M; Varghese, Mathai, Canadian Journal of Mathematics-Journal Canadien de Mathematiques 52 (695–736) 2000 |
D-Branes, B-Fields and twisted K-theory
Bouwknegt, Pier; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (1–11) 2000 |
Deformations of carbon-fiber-reinforced yacht masts
Clements, David; Cooke, Tristrom, Journal of Engineering Mathematics 37 (11–25) 2000 |
Extensional fall of a very viscous fluid drop
Stokes, Yvonne; Tuck, Ernest; Schwartz, L, Quarterly Journal of Mechanics and Applied Mathematics 53 (565–582) 2000 |
Global obstructions to gauge-invariance in chiral gauge theory on the lattice
Adams, David, Nuclear Physics B 589 (633–656) 2000 |
Inequalities for convex sets
Scott, Paul; Awyong, P-W, Journal of Inequalities in Pure and Applied Mathematics 1 (1–6) 2000 |
Inequalities for differentiable mappings with application to special means and quadrature formulae
Pearce, Charles; Pecaric, Josip, Applied Mathematics Letters 13 (51–55) 2000 |
Multivariate Hardy-type inequalities
Hanjs, Z; Pearce, Charles; Pecaric, Josip, Tamkang Journal of Mathematics 31 (149–158) 2000 |
Nonexistence results for the Korteweg-de Vries and Kadomtsev-Petviashvili equations
Joshi, Nalini; Petersen, J; Schubert, Luke Mark, Studies in Applied Mathematics 105 (361–374) 2000 |
Notes on Seiberg-Witten-Floer theory
Carey, Alan; Wang, Bai-Ling, Contemporary Mathematics 258 (71–85) 2000 |
On unbounded p-summable Fredholm modules
Carey, Alan; Phillips, J; Sukochev, Fedor, Advances in Mathematics 151 (140–163) 2000 |
Reciprocal link for 2 + 1-dimensional extensions of shallow water equations
Hone, Andrew, Applied Mathematics Letters 13 (37–42) 2000 |
Refinements of Jensen's inequality
Brnetic, I; Pearce, Charles; Pecaric, Josip, Tamkang Journal of Mathematics 31 (63–69) 2000 |
Remarks on a variable-coefficient sine-gordon equation
Hone, Andrew, Applied Mathematics Letters 13 (83–84) 2000 |
The unified treatment of some inequalities of Ostrowski and Simpson types
Culjak, V; Pearce, Charles; Pecaric, Josip, Soochow Journal of Mathematics 26 (377–390) 2000 |
Weak and generalized solutions to abstract stochastic equations
Melnikova, I; Filinkov, Alexei, Doklady Mathematics 62 (373–377) 2000 |
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