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Search the School of Mathematical Sciences
People matching "Differential geometry"
Courses matching "Differential geometry"
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Differential Equations 
Differential equations are of basic importance in applied mathematics
because many physical laws and relations can be formulated as a differential
equation. As the course unfolds you will learn to master some of the methods
needed to solve both ordinary differential equations and partial differential
equations. Topics covered in the course will include: first order ordinary differential
equations (ODEs), second order linear ODEs, higher order ODEs, numerical
techniques for solving ODEs, systems of ODEs, series solutions of ODEs,
Laplace transforms, Fourier analysis and linear second order partial
differential equations.
More about this course...
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Differential Equations III
Methods for the solution of initial value problems for systems of first order linear and non- linear ordinary differential equations. This will include some discussion of the existence of solutions and of numerical methods;
Techniques for the solution of two point boundary value problems for second order linear ordinary differential equations with variable coefficients. This includes the introduction of Green's Functions and use of eigenfunction expansions; Classification of partial differential equations and the solution of boundary value problems for these equations including the methods of
(a) reduction to ordinary differential equations by separation of variables
(b) the use of transform methods
(c) the method of characteristics.
More about this course...
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Differential Geometry
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...
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Fields and Geometry III
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...
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Events matching "Differential geometry"
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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...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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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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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...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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Direct "delay" reductions of the Toda equation
13:10 Fri 23 Jan 09 | School Board Room | Prof Nalini Joshi | University of Sydney
Abstract...A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as
delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated to this equation is obtained, also by reduction.
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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...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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Bibundles 13:10 Fri 6 Mar 09 | School Board Room | Prof Michael Murray | University of Adelaide |
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The index theorem for projective families of elliptic operators 13:10 Fri 13 Mar 09 | School Board Room | Prof Mathai Varghese | University of Adelaide |
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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...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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Classification and compact complex manifolds I 13:10 Fri 17 Apr 09 | School Board Room | A/Prof Nicholas Buchdahl | University of Adelaide |
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Classification and compact complex manifolds II 13:10 Fri 24 Apr 09 | School Board Room | A/Prof Nicholas Buchdahl | University of Adelaide |
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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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Four classes of complex manifolds 13:10 Fri 8 May 09 | School Board Room | A/Prof Finnur Larusson | University of Adelaide
Abstract...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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Lagrangian fibrations on holomorphic symplectic manifolds I: Holomorphic Lagrangian fibrations 13:10 Fri 5 Jun 09 | School Board Room | Dr Justin Sawon | Colorado State University
Abstract...A compact K{\"a}hler manifold $X$ is a holomorphic symplectic manifold if it admits a non-degenerate holomorphic two-form $\sigma$. According to a theorem of Matsushita, fibrations on $X$ must be of a very restricted type: the fibres must be Lagrangian with respect to $\sigma$ and the generic fibre must be a complex torus. Moreover, it is expected that the base of the fibration must be complex projective space, and this has been proved by Hwang when $X$ is projective. The simplest example of these {\em Lagrangian fibrations\/} are elliptic K3 surfaces. In this talk we will explain the role of elliptic K3s in the classification of K3 surfaces, and the (conjectural) generalization to higher dimensions.
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Chern-Simons classes on loop spaces and diffeomorphism groups 13:10 Fri 12 Jun 09 | School Board Room | Prof Steve Rosenberg | Boston University
Abstract...The loop space LM of a Riemannian manifold M comes with a family of Riemannian metrics indexed by a Sobolev parameter. We can construct characteristic classes for LM using the Wodzicki residue instead of the usual matrix trace. The Pontrjagin classes of LM vanish, but the secondary or Chern-Simons classes may be nonzero and may distinguish circle actions on M. There are similar results for diffeomorphism groups of manifolds.
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Lagrangian fibrations on holomorphic symplectic manifolds II: Existence of Lagrangian fibrations 13:10 Fri 19 Jun 09 | School Board Room | Dr Justin Sawon | Colorado State University
Abstract...The Hilbert scheme ${\mathrm Hilb}^nS$ of points on a K3 surface $S$ is a well-known holomorphic symplectic manifold. When does ${\mathrm Hilb}^nS$ admit a Lagrangian fibration? The existence of a Lagrangian fibration places some conditions on the Hodge structure, since the pull back of a hyperplane from the base gives a special divisor on ${\mathrm Hilb}^nS$, and in turn a special divisor on $S$. The converse is more difficult, but using Fourier-Mukai transforms we will show that if $S$ admits a divisor of a certain degree then ${\mathrm Hilb}^nS$ admits a Lagrangian fibration.
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Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations 15:10 Fri 19 Jun 09 | LG29 | Prof. Eckhard Platen | University of Technology, Sydney
Abstract...This paper introduces a new class of numerical
schemes for the pathwise approximation of solutions of stochastic
differential equations (SDEs). The proposed family of strong
predictor-corrector Euler methods are designed to handle scenario
simulation of solutions of SDEs. It has the potential to overcome
some of the numerical instabilities that are often experienced
when using the explicit Euler method. This is of importance, for
instance, in finance where martingale dynamics arise for solutions
of SDEs with multiplicative diffusion coefficients. Numerical
experiments demonstrate the improved asymptotic stability
properties of the proposed symmetric predictor-corrector Euler
methods.
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Lagrangian fibrations on holomorphic symplectic manifolds III: Holomorphic coisotropic reduction 13:10 Fri 26 Jun 09 | School Board Room | Dr Justin Sawon | Colorado State University
Abstract...Given a certain kind of submanifold $Y$ of a symplectic manifold $(X,\omega)$ we can form its coisotropic reduction as follows. The null directions of $\omega|_Y$ define the characteristic foliation $F$ on $Y$. The space of leaves $Y/F$ then admits a symplectic form, descended from $\omega|_Y$. Locally, the coisotropic reduction $Y/F$ looks just like a symplectic quotient. This construction also work for holomorphic symplectic manifolds, though one of the main difficulties in practice is ensuring that the leaves of the foliation are compact. We will describe a criterion for compactness, and apply coisotropic reduction to produce a classification result for Lagrangian fibrations by Jacobians.
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Another proof of Gaboriau-Popa 13:10 Fri 3 Jul 09 | School Board Room | Prof Greg Hjorth | University of Melbourne
Abstract...Gaboriau and Popa showed that a non-abelian free group on finitely many generators has continuum many measure preserving, free, ergodic, actions on standard Borel probability spaces. The original proof used the notion of property (T). I will sketch how this can be replaced by an elementary, and apparently new, dynamical property.
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Generalizations of the Stein-Tomas restriction theorem 13:10 Fri 7 Aug 09 | School Board Room | Prof Andrew Hassell | Australian National University
Abstract...The Stein-Tomas restriction theorem says that the
Fourier transform of a function in L^p(R^n) restricts to an
L^2 function on the unit sphere, for p in some range [1, 2(n+1)/(n+3)].
I will discuss geometric generalizations of this result, by interpreting
it as a property of the spectral measure of the Laplace operator on
R^n, and then generalizing to the Laplace-Beltrami operator on
certain complete Riemannian manifolds. It turns out that dynamical
properties of the geodesic flow play a crucial role in determining whether
a restriction-type theorem holds for these manifolds.
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Asymmetric Cantor measures and sumsets 13:10 Fri 14 Aug 09 | School Board Room | Prof Gavin Brown | Royal Institution of Australia and University of Adelaide |
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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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Moduli spaces of stable holomorphic vector bundles 13:10 Fri 28 Aug 09 | School Board Room | Dr Nicholas Buchdahl | University of Adelaide |
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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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Covering spaces and algebra bundles 13:10 Fri 11 Sep 09 | School Board Room | Prof Keith Hannabuss | University of Oxford
Abstract...Bundles of C*-algebras over a topological space M can be classified by a Dixmier-Douady obstruction in H^3(M,Z). This talk will describe some recent work with Mathai investigating the relationship between algebra bundles on M and on its covering space, where there can be no obstruction, particularly when there is a group acting on M.
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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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A Fourier-Mukai transform for invariant differential cohomology 13:10 Fri 9 Oct 09 | School Board Room | Mr Richard Green | University of Adelaide
Abstract...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...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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Building centralisers in ~A_2 groups 13:10 Fri 23 Oct 09 | School Board Room | Prof Guyan Robertson | University of Newcastle, UK |
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Analytic torsion for twisted de Rham complexes 13:10 Fri 30 Oct 09 | School Board Room | Prof Mathai Varghese | University of Adelaide
Abstract...We define analytic torsion for the twisted de Rham complex, consisting of differential forms on a compact Riemannian manifold X with coefficients in a flat vector bundle E, with a differential given by a flat connection on E plus a closed odd degree differential form on X. The definition in our case is more complicated than in the case discussed by Ray-Singer, as it uses pseudodifferential operators. We show that this analytic torsion is independent of the choice of metrics on X and E, establish some basic functorial properties, and compute it in many examples. We also establish the relationship of an invariant version of analytic torsion for T-dual circle bundles with closed 3-form flux. This is joint work with Siye Wu.
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TBA 11:10 Mon 14 Dec 09 | School Board Room | Dr Nicole Lemire | University of Western Ontario, Canada |
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TBA 13:10 Mon 14 Dec 09 | School Board Room | Dr Graham Denham | University of Western Ontario, Canada |
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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
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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
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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
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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
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TBA 13:10 Fri 29 Jan 10 | School Board Room | Prof Franc Forstneric | University of Ljubljana |
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TBA 13:10 Fri 5 Feb 10 | School Board Room | Prof Franc Forstneric | University of Ljubljana |
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Some sinc sums and integrals (to be confirmed) 13:10 Fri 16 Apr 10 | School Board Room | Prof Jonathan Borwein | University of Newcastle
Abstract...I shall mix classical analyis and modern computation to study integrals of powers of sinc functions and related objects. Along the way I shall demonstrate some remarkable false identities and some almost-as-remarkable true ones. This talk is based on joint research with various researchers aged eighteen (Bernard Mares) to eighty-five (David Borwein).
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News matching "Differential geometry"
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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 for full details. Posted Wed 17 Sep 08.
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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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Publications matching "Differential geometry"
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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 |
Portfolio risk minimization and differential games
Elliott, Robert; Siu, T, Nonlinear Analysis-Theory Methods & Applications In Press (–) 2009 |
A markovian regime-switching stochastic differential game for portfolio risk minimization
Elliott, Robert; Siu, T, 2008 American Control Conference, Washington 11/06/08 |
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 |
Dessins d'enfants and differential equations
Larusson, Finnur; Sadykov, T, St Petersburg Mathematical Journal 19 (1003–1014) 2008 |
Equivariant and fractional index of projective elliptic operators
Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 78 (465–473) 2008 |
Invariant differential pairings
Kroeske, Jens, Universitas Comeniana. Acta Mathematica 77 (215–244) 2008 |
The basic bundle gerbe on unitary groups
Murray, Michael; Stevenson, Daniel, Journal of Geometry and Physics 58 (1571–1590) 2008 |
Model subgrid microscale interactions to accurately discretise stochastic partial differential equations.
Roberts, Anthony John, |
Monogenic functions in conformal geometry
Eastwood, Michael; Ryan, J, Symmetry, Integrability and Geometry: Methods and Applications 84 (1–14) 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 |
Computer algebra derives normal forms of stochastic differential equations
Roberts, Anthony John, |
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 |
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 |
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 |
Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation
Roberts, Anthony John, |
Dynamics of CP1 lumps on a cylinder
Romao, Nuno, Journal of Geometry and Physics 54 (42–76) 2005 |
The index of projective families of elliptic operators
Varghese, Mathai; Melrose, R; Singer, I, Geometry & Topology Online 9 (341–373) 2005 |
On the analysis of a case-control study with differential measurement error
Glonek, Garique, 20th International Workshop on Statistical Modelling, Sydney, Australia 10/07/05 |
Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations
Roberts, Anthony John, |
A geometrical construction of the oval(s) associated with an a-flock
Brown, Matthew; Thas, J, Advances in Geometry 4 (9–17) 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 |
Partial differential equations
Van Der Hoek, John, Workshop on Mathematical Methods in Finance (2004), Melbourne, Vic, 2004 07/06/04 |
Towards a Classification of Homogeneous Tube Domains in C(4)
Eastwood, Michael; Ezhov, Vladimir; Isaev, A, Journal of Differential Geometry 68 (553–569) 2004 |
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 |
Stochastic Differential Equations in Hilbert Spaces
Filinkov, Alexei; Maizurna, Isna; Sorenson, J; Van Der Hoek, John, chapter in Applicable Mathematics in the Golden Age (Morgan & Claypool) 32–169, 2003 |
A step towards holistic discretisation of stochastic partial differential equations
Roberts, Anthony John, The ANZIAM Journal 45 (C1–C15) 2003 |
Evidence for a Differential Cellular Distribution of Inward Rectifier K Channels in the Rat Isolated Mesenteric Artery
Crane, Glenis Jayne; Walker, S; Dora, K; Garland, C, Journal of Vascular Research 40 (159–168) 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 |
Differential equations in spaces of abstract stochastic distributions
Filinkov, Alexei; Sorensen, Julian, Stochastics and Stochastic Reports 72 (129–173) 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 |
Some special geometry in dimension six
Eastwood, Michael; Cap, A, Czech Winter School on Geometry and Physics (22nd: 2002:, Srn'i, Czechoslovakia), |
Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models
Melnik, R; Roberts, Anthony John; Thomas, K, Computational Mechanics 29 (16–26) 2002 |
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 |
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 |
Non-Schlesinger deformations of ordinary differential equations with rational coefficients
Kitaev, Alexandre, Journal of Physics A: Mathematical and Theoretical (Print Edition) 34 (2259–2272) 2001 |
Truncation-type methods and Bcklund transformations for ordinary differential equations: The third and fifth Painlev equations
Gordoa, P; Joshi, Nalini; Pickering, A, Glasgow Mathematical Journal 43A (23–32) 2001 |
Conformally invariant differential operators on spin bundles
Eastwood, Michael, chapter in Further advances in twistor theory. Vol. III, Curved twistor spaces (Chapman & Hall/CRC) 72–74, 2001 |
A note on higher cohomology groups of Khler quotients
Wu, Siye, Annals of Global Analysis and Geometry 18 (569–576) 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 |
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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