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People matching "Index theory and noncommutative geometry"
Courses matching "Index theory and noncommutative geometry"
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Differential Geometry  [51]
This course is part of the course offerings for Honours Pure Mathematics (Level IV).
Assumed knowledge: Multivariable Calculus. A basic understanding of topology as would be obtained from Analysis & Topology is helpful but not mandatory. A basic understanding of abstract linear algebra is also helpful, but the necessary material will developed during the course.
1. Review of multivariable calculus; linear algebra.
2. Differential forms in Euclidean space: exterior derivative, pull-back, integral, Poincar'e Lemma.
3. Manifolds: Tangent spaces, differentiable functions, the derivative, differential forms, Stokes' theorem.
4. de Rham and Cech cohomology.
5. Vector bundles and connections: Vector bundles, connections, curvature, Chern classes.
6. The Gauss-Bonnet theorem: The Euler characteristic of a surface, the Gauss-Bonnet theorem.
More about this course... [52]
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Distribution Theory and PDEs [53]
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.
More about this course... [54]
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Fields and Geometry III [55]
This course is an investigation of the
relationship between the concepts of "number" and "geometry". In the
traditional plane geometry of drawing figures on a piece of paper we
can use two real number coordinates to describe the plane. Lines,
circles and many other geometrical objects can be specified using
equations on the coordinates and their geometrical properties
determined by calculations with real numbers. In this way the
geometrical properties of the plane are reflected in the algebraic
properties of the real numbers, and conversely. In this course the
idea of the connection between number and geometry is pursued using
more general number systems and geometries.
The first part of the course generalises the real numbers to a
mathematical structure called a field. A field is a set of elements in
which we can add, subtract, multiply and divide; examples being the
real numbers, complex numbers and the rational numbers. Properties and
constructions of fields will be investigated in detail. Of particular
interest will be the examples of fields that have a finite number of
elements. Finite fields have many applications, particularly in
Information Security where the understanding of finite fields is
fundamental to many codes and cryptosystems.
The second part of the course considers projective geometries.
Projective geometry is one of the important modern geometries
introduced in the 19th century. The history of geometry is
fascinating, and we discuss this briefly. Projective geometry is more
general than our usual Euclidean geometry, and it has useful
applications in Information Security, Statistics, Computer Graphics
and Computer Vision
The focus will be primarily on projective planes. They will be
introduced axiomatically and then examples constructed by using fields
as coordinates (although not coordinates in the Cartesian sense).
Once we have set up our tools, we discuss some familiar concepts (such
as conics and transformations) in the context of projective planes.
We will then consider projective spaces of general (finite) dimension
and briefly axiomatic generalisations of projective geometries.
Finite projective geometries provide an excellent opportunity for
the study of geometries with a simple structure, and are a good
setting to enhance problem solving skills. Fields: fields, polynomials
rings, extensions of fields; automorphisms of fields, the structure of
a finite field.
Projective Geometry: projective planes, homogeneous coordinates,
field planes, collineations of projective planes, conics in field
planes, projective geometry of general dimension.
More about this course... [56]
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Information Theory [59]
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.
More about this course... [60]
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Events matching "Index theory and noncommutative geometry"
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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... [61]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... [62]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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Homological algebra and applications - a historical survey 15:10 Fri 19 May 06 | G08, Mathematics Building, University of Adelaide | Prof. Amnon Neeman
Abstract... [63]Homological algebra is a curious branch of
mathematics; it is a powerful tool which has been used in many diverse
places, without any clear understanding why it should be so useful.
We will give a list of applications, proceeding chronologically: first
to topology, then to complex analysis, then to algebraic geometry,
then to commutative algebra and finally (if we have time) to
non-commutative algebra. At the end of the talk I hope to be able to
say something about the part of homological algebra on which I have
worked, and its applications. That part is derived categories.
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Good and Bad Vibes 15:10 Fri 23 Feb 07 | G08, Mathematics Building, University of Adelaide | Prof. Maurice Dodson
Abstract... [65]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.
Media for this event... [66]
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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... [67]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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Add one part chaos, one part topology, and stir well... 13:10 Fri 19 Oct 07 | Engineering North 132 | Dr Matt Finn
Abstract... [69]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.
Media for this event... [70]
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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... [71]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... [72]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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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... [73]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... [74]
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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Mathematical modelling of blood flow in curved arteries 15:10 Fri 12 Sep 08 | G03, Napier Building, University of Adelaide | Dr Jennifer Siggers | Imperial College London
Abstract... [75]Atherosclerosis, characterised by plaques, is the most common arterial
disease. Plaques tend to develop in regions of low mean wall shear
stress, and regions where the wall shear stress changes direction during
the course of the cardiac cycle. To investigate the effect of the
arterial geometry and driving pressure gradient on the wall shear stress
distribution we consider an idealised model of a curved artery with
uniform curvature. We assume that the flow is fully-developed and seek
solutions of the governing equations, finding the effect of the
parameters on the flow and wall shear stress distribution. Most
previous work assumes the curvature ratio is asymptotically small;
however, many arteries have significant curvature (e.g. the aortic arch
has curvature ratio approx 0.25), and in this work we consider in
particular the effect of finite curvature.
We present an extensive analysis of curved-pipe flow driven by a steady
and unsteady pressure gradients. Increasing the curvature causes the
shear stress on the inside of the bend to rise, indicating that the risk
of plaque development would be overestimated by considering only the
weak curvature limit.
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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... [76]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... [77]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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Noncommutative geometry of odd-dimensional quantum spheres 13:10 Fri 27 Feb 09 | School Board Room | Dr Partha Chakraborty | University of Adelaide
Abstract... [78]We will report on our attempts to understand noncommutative geometry in the lights of the example of quantum spheres. We will see how to produce an equivariant fundamental class and also indicate some of the limitations of isospectral deformations.
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Geometric analysis on the noncommutative torus 13:10 Fri 20 Mar 09 | School Board Room | Prof Jonathan Rosenberg | University of Maryland
Abstract... [79]Noncommutative geometry (in the sense of Alain Connes) involves
replacing a conventional space by a "space" in which the algebra of
functions is noncommutative. The simplest truly non-trivial
noncommutative manifold is the noncommutative 2-torus, whose algebra
of functions is also called the irrational rotation algebra. I will
discuss a number of recent results on geometric analysis on the
noncommutative torus, including the study of nonlinear noncommutative
elliptic PDEs (such as the noncommutative harmonic map equation) and
noncommutative complex analysis (with noncommutative elliptic
functions).
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Understanding optimal linear transient growth in complex-geometry flows 15:00 Fri 27 Mar 09 | Napier LG29 | Associate Professor Hugh Blackburn | Monash University |
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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... [80]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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Four classes of complex manifolds 13:10 Fri 8 May 09 | School Board Room | A/Prof Finnur Larusson | University of Adelaide
Abstract... [81]We introduce the four classes of complex manifolds defined by having few or many holomorphic maps to or from the complex plane. Two of these classes have played an important role in complex geometry for a long time. A third turns out to be too large to be of much interest. The fourth class has only recently emerged from work of Abel Prize winner Mikhail Gromov.
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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... [82]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... [83]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... [84]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... [85]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... [86]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... [87]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... [88]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... [89]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... [90]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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A Fourier-Mukai transform for invariant differential cohomology 13:10 Fri 9 Oct 09 | School Board Room | Mr Richard Green | University of Adelaide
Abstract... [91]Fourier-Mukai transforms are a geometric analogue of integral transforms playing
an important role in algebraic geometry. Their name derives from the
construction of Mukai involving the Poincare line bundle associated to an
abelian variety. In this talk I will discuss recent work looking at an analogue
of this original Fourier-Mukai transform in the context of differential
geometry, which gives an isomorphism between the invariant differential
cohomology of a real torus and its dual.
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Irreducible subgroups of SO(2,n) 13:10 Fri 16 Oct 09 | School Board Room | Dr Thomas Leistner | University of Adelaide
Abstract... [92]Berger's classification of irreducibly represented Lie groups that can occur as holonomy groups of semi-Riemannian manifolds is a remarkable result of modern differential geometry. What is remarkable about it is that it is so short and that only so few types of geometry can occur. In Riemannian signature this is even more remarkable, taking into account that any representation of a compact Lie group admits a positive definite invariant scalar product. Hence, for any not too small n there is an abundance of irreducible subgroups of SO(n). We show that in other signatures the situation is quite different with, for example, SO(1,n) having no proper irreducible subgroups. We will show how this and the corresponding result about irreducible subgroups of SO(2,n) follows from the Karpelevich-Mostov theorem. (This is joint work with Antonio J. Di Scala, Politecnico di Torino.)
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Is the price really right? 12:10 Thu 22 Oct 09 | Napier 210 | Mr Sam Cohen | University of Adelaide
Abstract... [94]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... [95]
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Group actions in complex geometry, I and II 13:10 Fri 8 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
Media for this event... [97]
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Group actions in complex geometry, III and IV 10:10 Fri 15 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
Media for this event... [99]
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Group actions in complex geometry, V and VI 10:10 Fri 22 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
Media for this event... [101]
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Group actions in complex geometry, VII and VIII 10:10 Fri 29 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
Media for this event... [103]
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News matching "Index theory and noncommutative geometry"
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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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Stoneham Prize The inaugural Stoneham Prize, awarded for the best poster by a graduate student in the first two years of their candidature, was awarded on the 4th of April. The winner was Ric Green, for his poster "What is Geometry?". Two Viewers' Choice prizes were also awarded to Ray Vozzo for his poster "The 7 Bridges of Koenigsberg - The 1st Theorem in Topology" and David Butler for his poster "The Queen of Hearts Plays Noughts and Crosses". Posted Sun 13 Apr 08.
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Workshop on Complex Geometry The Institute for Geometry and its Applications will host a Workshop on Complex Geometry at the University of Adelaide from Monday 16 February to Friday 20 February 2009. Click here [104] for full 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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 [105] |
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... [106]
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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 "Index theory and noncommutative geometry"
| Publications |
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A characterisation of the lines external to an oval cone in PG(3, q), q even
Barwick, Susan; Butler, David, Journal of Geometry 93 (21–27) 2009 |
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 maximum size of the intersection of two ovoids
Butler, David, Journal of Combinatorial Theory Series A 116 (242–245) 2009 |
Metric connections in projective differential geometry
Eastwood, Michael; Matveev, V, Symmetries and Overdetermined Systems of Partial Differential Equations, USA 17/07/08 |
Notes on projective differential geometry
Eastwood, Michael, Symmetries and Overdetermined Systems of Partial Differential Equations, USA 17/07/08 |
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 |
D-branes, RR-fields and duality on noncommutative manifolds
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Communications in Mathematical Physics 277 (643–706) 2008 |
Equivariant and fractional index of projective elliptic operators
Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 78 (465–473) 2008 |
The basic bundle gerbe on unitary groups
Murray, Michael; Stevenson, Daniel, Journal of Geometry and Physics 58 (1571–1590) 2008 |
Monogenic functions in conformal geometry
Eastwood, Michael; Ryan, J, Symmetry, Integrability and Geometry: Methods and Applications 84 (1–14) 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 |
On the geometry of regular hyperbolic fibrations
Brown, Matthew; Ebert, G; Luyckz, D, European Journal of Combinatorics 28 (1626–1636) 2007 |
Projective ovoids and generalized quadrangles
Brown, Matthew, Advances in Geometry 7 (65–81) 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 |
Symmetries and invariant differential pairings
Eastwood, Michael, Symmetry, Integrability and Geometry: Methods and Applications 113 (1–10) 2007 |
T-Duality in type II string theory via noncommutative geometry and beyond
Varghese, Mathai, Progress of Theoretical Physics Supplement 171 (237–257) 2007 |
Towards the fractional quantum Hall effect: a noncummutative geometry perspective
Marcolli, M; Varghese, Mathai, chapter in Noncommutative geometry and number theory (Vieweg, Springer Science+Business Media) 235–262, 2006 |
Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds
Leistner, Thomas, Differential Geometry and its Applications 24 (458–478) 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 |
Formal adjoints and canonical form for linear operations
Eastwood, Michael; Gover, A, Conformal Geometry and Dynamics 10 (285–287) 2006 |
Fractional analytic index
Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 74 (265–292) 2006 |
Quantum Hall effect and noncommutative geometry
Carey, Alan; Hannabuss, K; Varghese, Mathai, Journal of Geometry and Symmetry in Physics 6 (16–36) 2006 |
Screen bundles of Lorentzian manifolds and some generalisations of pp-waves
Leistner, Thomas, Journal of Geometry and Physics 56 (2117–2134) 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 |
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
Varghese, Mathai; Rosenberg, J, Advances in Theoretical and Mathematical Physics 10 (123–158) 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 |
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 |
Dynamics of CP1 lumps on a cylinder
Romao, Nuno, Journal of Geometry and Physics 54 (42–76) 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 |
M-theory and characteristic classes
Sati, Hicham, The Journal of High Energy Physics (Online Editions) 8 (020-1–020-8) 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 |
T-duality for torus bundles with H-fluxes via noncommutative topology
Varghese, Mathai; Rosenberg, J, Communications in Mathematical Physics 253 (705–721) 2005 |
The index of projective families of elliptic operators
Varghese, Mathai; Melrose, R; Singer, I, Geometry & Topology Online 9 (341–373) 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 |
A geometrical construction of the oval(s) associated with an a-flock
Brown, Matthew; Thas, J, Advances in Geometry 4 (9–17) 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 |
Gerbes, Clifford Modules and the index theorem
Murray, Michael; Singer, Michael, Annals of Global Analysis and Geometry 26 (355–367) 2004 |
Holonomy on D-branes
Carey, Alan; Johnson, Stuart; Murray, Michael, Journal of Geometry and Physics 52 (186–216) 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 |
M-theory, type IIA superstrings, and elliptic cohomology
Kriz, I; Sati, Hicham, Advances in Theoretical and Mathematical Physics 8 (345–394) 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 |
Measure Theory and Filtering: Introduction and Applications
Aggoun, L; Elliott, Robert, (Cambridge University Press) 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 |
Towards a Classification of Homogeneous Tube Domains in C(4)
Eastwood, Michael; Ezhov, Vladimir; Isaev, A, Journal of Differential Geometry 68 (553–569) 2004 |
Geometric means, index mappings and entropy
Comanescu, D; Dragomir, S; Pearce, Charles, chapter in Inequality theory and applications - Volume 3 (Nova Science Publishers) 85–96, 2003 |
Geometric means, index mappings and supermultiplicativity
Pearce, Charles; Dragomir, S; Comanescu, D, chapter in Inequality theory and applications - Volume 2 (Nova Science Publishers) 193–201, 2003 |
A general fractional white noise theory and applications to finance
Elliott, Robert; Van Der Hoek, John, Mathematical Finance 13 (301–330) 2003 |
Chern character in twisted K-theory: Equivariant and holomorphic cases
Varghese, Mathai; Stevenson, Daniel, Communications in Mathematical Physics 236 (161–186) 2003 |
Compact Khler surfaces with trivial canonical bundle
Buchdahl, Nicholas, Annals of Global Analysis and Geometry 23 (189–204) 2003 |
Edge of the wedge theory in hypo-analytic manifolds
Eastwood, Michael; Graham, C, Communications in Partial Differential Equations 28 (2003–2028) 2003 |
Hyperbolic monopoles and holomorphic spheres
Murray, Michael; Norbury, Paul; Singer, Michael, Annals of Global Analysis and Geometry 23 (101–128) 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 |
The geometry and physics of the Seiberg-Witten equations
Wu, Siye, chapter in Geometric analysis and applications to quantum field theory (Birkhauser) 157–203, 2002 |
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 |
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 |
The Andr/Bruck and Bose representation of conics in Baer subplanes of PG(2, q2)
Quinn, Catherine, Journal of Geometry 74 (123–138) 2002 |
The universal gerbe, Dixmier-Douady class, and gauge theory
Carey, Alan; Mickelsson, J, Letters in Mathematical Physics 59 (47–60) 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 |
Some special geometry in dimension six
Eastwood, Michael; Cap, A, Czech Winter School on Geometry and Physics (22nd: 2002:, Srn'i, Czechoslovakia), |
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 proof of Atiyah's conjecture on configurations of four points in Euclidean three-space
Eastwood, Michael; Norbury, Paul, Geometry & Topology 5 (885–893) 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 |
Direct computation of the performance index for an optimally controlled active suspension with preview applied to a half-car model
Thompson, A; Pearce, Charles, Vehicle System Dynamics 35 (121–137) 2001 |
Equivariant Seiberg-Witten Floer homology
Marcolli, M; Wang, Bai-Ling, Communications in Analysis and Geometry 9 (451–639) 2001 |
Generalising a characterisation of Hermitian curves
Barwick, Susan; Quinn, Catherine, Journal of Geometry 70 (1–7) 2001 |
Linearised cavity theory with smooth detachment
Haese, Peter, Australian Mathematical Society Gazette 28 (187–193) 2001 |
On the continuum limit of fermionic topological charge in lattice gauge theory
Adams, David, Journal of Mathematical Physics 42 (5522–5533) 2001 |
Performance index for a preview active suspension applied to a quarter-car model
Thompson, A; Pearce, Charles, Vehicle System Dynamics 35 (55–66) 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 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 |
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 note on higher cohomology groups of Khler quotients
Wu, Siye, Annals of Global Analysis and Geometry 18 (569–576) 2000 |
A remark of Schwarz's topological field theory
Adams, David; Prodanov, E, Letters in Mathematical Physics 51 (249–255) 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 |
D-Branes, B-Fields and twisted K-theory
Bouwknegt, Pier; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (1–11) 2000 |
Dirac operator index and topology of lattice gauge fields
Adams, David, Chinese Journal of Physics 38 (633–646) 2000 |
Global obstructions to gauge-invariance in chiral gauge theory on the lattice
Adams, David, Nuclear Physics B 589 (633–656) 2000 |
Local Constraints on Einstein-Weyl geometries: The 3-dimensional case
Eastwood, Michael; Tod, K, Annals of Global Analysis and Geometry 18 (1–27) 2000 |
Notes on Seiberg-Witten-Floer theory
Carey, Alan; Wang, Bai-Ling, Contemporary Mathematics 258 (71–85) 2000 |
The determination of ovoids of PG(3, q) containing a pointed conic
Brown, Matthew, Journal of Geometry 67 (61–72) 2000 |
Unitals which meet Baer subplanes in 1 modulo q points
Barwick, Susan; O'Keefe, Christine; Storme, L, Journal of Geometry 68 (16–22) 2000 |
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