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August 2019

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Professor Nigel Bean
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Dr David Green
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Professor Finnur Larusson
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Events matching "Analytic torsion for twisted de Rham complexes"

Analytic torsion for twisted de Rham complexes
13:10 Fri 30 Oct, 2009 :: School Board Room :: Prof Mathai Varghese :: University of Adelaide

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.
Random walk integrals
13:10 Fri 16 Apr, 2010 :: School Board Room :: Prof Jonathan Borwein :: University of Newcastle

Following Pearson in 1905, we study the expected distance of a two-dimensional walk in the plane with unit steps in random directions---what Pearson called a "ramble". A series evaluation and recursions are obtained making it possible to explicitly determine this distance for small number of steps. Closed form expressions for all the moments of a 2-step and a 3-step walk are given, and a formula is conjectured for the 4-step walk. Heavy use is made of the analytic continuation of the underlying integral.
A classical construction for simplicial sets revisited
13:10 Fri 27 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Danny Stevenson :: University of Glasgow

Simplicial sets became popular in the 1950s as a combinatorial way to study the homotopy theory of topological spaces. They are more robust than the older notion of simplicial complexes, which were introduced for the same purpose. In this talk, which will be as introductory as possible, we will review some classical functors arising in the theory of simplicial sets, some well-known, some not-so-well-known. We will re-examine the proof of an old theorem of Kan in light of these functors. We will try to keep all jargon to a minimum.
On some applications of higher Quillen K'-theory
13:10 Fri 3 Sep, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Snigdhayan Mahanta :: University of Adelaide

In my previous talk I introduced a functor from the category of k-algebras (k field) to abelian groups, called KQ-theory. In this talk I will explain its relationship with topological (homological) T-dualities and twisted K-theory.
IGA-AMSI Workshop: Dirac operators in geometry, topology, representation theory, and physics
10:00 Mon 18 Oct, 2010 :: 7.15 Ingkarni Wardli :: Prof Dan Freed :: University of Texas, Austin

Lecture Series by Dan Freed (University of Texas, Austin). Dirac introduced his eponymous operator to describe electrons in quantum theory. It was rediscovered by Atiyah and Singer in their study of the index problem on manifolds. In these lectures we explore new theorems and applications. Several of these also involve K-theory in its recent twisted and differential variations. These lectures will be supplemented by additional talks by invited speakers. For more details, please see the conference webpage:
What is a p-adic number?
12:10 Mon 28 Feb, 2011 :: 5.57 Ingkarni Wardli :: Alexander Hanysz :: University of Adelaide

The p-adic numbers are: (a) something that visiting seminar speakers invoke when the want to frighten the audience; (b) a fascinating and useful concept in modern algebra; (c) alphabetically just before q-adic numbers? In this talk I hope to convince the audience that option (b) is worth considering. I will begin by reviewing how we get from integers via rational numbers to the real number system. Then we'll look at how this process can be "twisted" to produce something new.
Real analytic sets in complex manifolds I: holomorphic closure dimension
13:10 Fri 4 Mar, 2011 :: Mawson 208 :: Dr Rasul Shafikov :: University of Western Ontario

After a quick introduction to real and complex analytic sets, I will discuss possible notions of complex dimension of real sets, and then discuss a structure theorem for the holomorphic closure dimension which is defined as the dimension of the smallest complex analytic germ containing the real germ.
Real analytic sets in complex manifolds II: complex dimension
13:10 Fri 11 Mar, 2011 :: Mawson 208 :: Dr Rasul Shafikov :: University of Western Ontario

Given a real analytic set R, denote by A the subset of R of points through which there is a nontrivial complex variety contained in R, i.e., A consists of points in R of positive complex dimension. I will discuss the structure of the set A.
Lattices in exotic groups
15:10 Fri 18 Mar, 2011 :: 7.15 Ingkarni Wardli :: Dr Anne Thomas :: University of Sydney

A lattice in a locally compact group G is a discrete subgroup of cofinite volume. Lattices in Lie groups are well-studied, but little is known about lattices in other, "exotic", locally compact groups. Examples of exotic groups include isometry groups of trees, buildings, polyhedral complexes and CAT(0) spaces, and Kac-Moody groups. We will survey known results, which include both rigidity and surprising examples of flexibility, and discuss the wide range of tools used to investigate lattices in these non-classical settings.
Modelling of Hydrological Persistence in the Murray-Darling Basin for the Management of Weirs
12:10 Mon 4 Apr, 2011 :: 5.57 Ingkarni Wardli :: Aiden Fisher :: University of Adelaide

The lakes and weirs along the lower Murray River in Australia are aggregated and considered as a sequence of five reservoirs. A seasonal Markov chain model for the system will be implemented, and a stochastic dynamic program will be used to find optimal release strategies, in terms of expected monetary value (EMV), for the competing demands on the water resource given the stochastic nature of inflows. Matrix analytic methods will be used to analyse the system further, and in particular enable the full distribution of first passage times between any groups of states to be calculated. The full distribution of first passage times can be used to provide a measure of the risk associated with optimum EMV strategies, such as conditional value at risk (CVaR). The sensitivity of the model, and risk, to changing rainfall scenarios will be investigated. The effect of decreasing the level of discretisation of the reservoirs will be explored. Also, the use of matrix analytic methods facilitates the use of hidden states to allow for hydrological persistence in the inflows. Evidence for hydrological persistence of inflows to the lower Murray system, and the effect of making allowance for this, will be discussed.
The Cauchy integral formula
12:10 Mon 9 May, 2011 :: 5.57 Ingkarni Wardli :: Stephen Wade :: University of Adelaide

In this talk I will explain a simple method used for calculating the Hilbert transform of an analytic function, and provide some assurance that this isn't a bad thing to do in spite of the somewhat ominous presence of infinite areas. As it turns out this type of integral is not without an application, as will be demonstrated by one application to a problem in fluid mechanics.
Twisted Morava K-theory
13:10 Fri 9 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Craig Westerland :: University of Melbourne

Morava's extraordinary K-theories K(n) are a family of generalized cohomology theories which behave in some ways like K-theory (indeed, K(1) is mod 2 K-theory). Their construction exploits Quillen's description of cobordism in terms of formal group laws and Lubin-Tate's methods in class field theory for constructing abelian extensions of number fields. Constructed from homotopy-theoretic methods, they do not admit a geometric description (like deRham cohomology, K-theory, or cobordism), but are nonetheless subtle, computable invariants of topological spaces. In this talk, I will give an introduction to these theories, and explain how it is possible to define an analogue of twisted K-theory in this setting. Traditionally, K-theory is twisted by a three-dimensional cohomology class; in this case, K(n) admits twists by (n+2)-dimensional classes. This work is joint with Hisham Sati.
Cohomology of higher-rank graphs and twisted C*-algebras
13:10 Fri 16 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Aidan Sims :: University of Wollongong

Higher-rank graphs and their $C^*$-algebras were introduced by Kumjian and Pask in 2000. They have provided a rich source of tractable examples of $C^*$-algebras, the most elementary of which are the commutative algebras $C(\mathbb{T}^k)$ of continuous functions on $k$-tori. In this talk we shall describe how to define the homology and cohomology of a higher-rank graph, and how to associate to each higher-rank graph $\Lambda$ and $\mathbb{T}$-valued cocycle on $\Lambda$ a twisted higher-rank graph $C^*$-algebra. As elementary examples, we obtain all noncommutative tori. This is a preleminary report on ongoing joint work with Alex Kumjian and David Pask.
Dirac operators on classifying spaces
13:10 Fri 28 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Pedram Hekmati :: University of Adelaide

The Dirac operator was introduced by Paul Dirac in 1928 as the formal square root of the D'Alembert operator. Thirty years later it was rediscovered in Euclidean signature by Atiyah and Singer in their seminal work on index theory. In this talk I will describe efforts to construct a Dirac type operator on the classifying space for odd complex K-theory. Ultimately the aim is to produce a projective family of Fredholm operators realising elements in twisted K-theory of a certain moduli stack.
Plurisubharmonic subextensions as envelopes of disc functionals
13:10 Fri 2 Mar, 2012 :: B.20 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide

I will describe new joint work with Evgeny Poletsky. We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation on the space of analytic discs in $X$ with boundary in $W$. The quotient is a complex manifold with a local biholomorphism to $X$, except it need not be Hausdorff. We use our disc formula to generalise Kiselman's minimum principle. We show that his infimum function is an example of a plurisubharmonic subextension.
The de Rham Complex
12:10 Mon 19 Mar, 2012 :: 5.57 Ingkarni Wardli :: Mr Michael Albanese :: University of Adelaide

The de Rham complex is of fundamental importance in differential geometry. After first introducing differential forms (in the familiar setting of Euclidean space), I will demonstrate how the de Rham complex elegantly encodes one half (in a sense which will become apparent) of the results from vector calculus. If there is time, I will indicate how results from the remaining half of the theory can be concisely expressed by a single, far more general theorem.
Index type invariants for twisted signature complexes
13:10 Fri 11 May, 2012 :: Napier LG28 :: Prof Mathai Varghese :: University of Adelaide

Atiyah-Patodi-Singer proved an index theorem for non-local boundary conditions in the 1970's that has been widely used in mathematics and mathematical physics. A key application of their theory gives the index theorem for signature operators on oriented manifolds with boundary. As a consequence, they defined certain secondary invariants that were metric independent. I will discuss some recent work with Benameur where we extend the APS theory to signature operators twisted by an odd degree closed differential form, and study the corresponding secondary invariants.
Noncommutative geometry and conformal geometry
13:10 Fri 24 Aug, 2012 :: Engineering North 218 :: Dr Hang Wang :: Tsinghua University

In this talk, we shall use noncommutative geometry to obtain an index theorem in conformal geometry. This index theorem follows from an explicit and geometric computation of the Connes-Chern character of the spectral triple in conformal geometry, which was introduced recently by Connes and Moscovici. This (twisted) spectral triple encodes the geometry of the group of conformal diffeomorphisms on a spin manifold. The crux of of this construction is the conformal invariance of the Dirac operator. As a result, the Connes-Chern character is intimately related to the CM cocycle of an equivariant Dirac spectral triple. We compute this equivariant CM cocycle by heat kernel techniques. On the way we obtain a new heat kernel proof of the equivariant index theorem for Dirac operators. (Joint work with Raphael Ponge.)
Complex analysis in low Reynolds number hydrodynamics
15:10 Fri 12 Oct, 2012 :: B.20 Ingkarni Wardli :: Prof Darren Crowdy :: Imperial College London

It is a well-known fact that the methods of complex analysis provide great advantage in studying physical problems involving a harmonic field satisfying Laplace's equation. One example is in ideal fluid mechanics (infinite Reynolds number) where the absence of viscosity, and the assumption of zero vorticity, mean that it is possible to introduce a so-called complex potential -- an analytic function from which all physical quantities of interest can be inferred. In the opposite limit of zero Reynolds number flows which are slow and viscous and the governing fields are not harmonic it is much less common to employ the methods of complex analysis even though they continue to be relevant in certain circumstances. This talk will give an overview of a variety of problems involving slow viscous Stokes flows where complex analysis can be usefully employed to gain theoretical insights. A number of example problems will be considered including the locomotion of low-Reynolds-number micro-organisms and micro-robots, the friction properties of superhydrophobic surfaces in microfluidics and problems of viscous sintering and the manufacture of microstructured optic fibres (MOFs).
Thin-film flow in helically-wound channels with small torsion
15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide

The study of flow in open helically-wound channels has application to many natural and industrial flows. We will consider laminar flow down helically-wound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steady-state flow that is independent of position along the axis of the channel, the flow solution may be determined in the two-dimensional cross section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier-Stokes equations. This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particle-laden thin-film flow in spiral channels will also be discussed.
Thin-film flow in helically-wound channels with small torsion
15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide

The study of flow in open helically-wound channels has application to many natural and industrial flows. We will consider laminar flow down helically-wound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steady-state flow that is independent of position along the axis of the channel, the flow solution may be determined in the two-dimensional cross section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity in terms of the free-surface shape. The latter satisfies an interesting non-linear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier-Stokes equations. This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particle-laden thin-film flow in spiral channels will also be discussed.
Twisted analytic torsion and adiabatic limits
13:10 Wed 5 Dec, 2012 :: Ingkarni Wardli B17 :: Mr Ryan Mickler :: University of Adelaide

We review Mathai-Wu's recent extension of Ray-Singer analytic torsion to supercomplexes. We explore some new results relating these two torsions, and how we can apply the adiabatic spectral sequence due to Forman and Farber's analytic deformation theory to compute some spectral invariants of the complexes involved, answering some questions that were posed in Mathai-Wu's paper.
Variation of Hodge structure for generalized complex manifolds
13:10 Fri 7 Dec, 2012 :: Ingkarni Wardli B20 :: Dr David Baraglia :: University of Adelaide

Generalized complex geometry combines complex and symplectic geometry into a single framework, incorporating also holomorphic Poisson and bi-Hermitian structures. The Dolbeault complex naturally extends to the generalized complex setting giving rise to Hodge structures in twisted cohomology. We consider the variations of Hodge structure and period mappings that arise from families of generalized complex manifolds. As an application we prove a local Torelli theorem for generalized Calabi-Yau manifolds.
Twistor theory and the harmonic hull
15:10 Fri 8 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Michael Eastwood :: Australian National University

Harmonic functions are real-analytic and so automatically extend as functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated conformal geometry. Nothing will be supposed about such matters: I shall base the constructions on an elementary yet mysterious formula of Bateman from 1904. This is joint work with Feng Xu.
Crystallographic groups I: the classical theory
12:10 Fri 17 May, 2013 :: Ingkarni Wardli B19 :: Dr Wolfgang Globke :: University of Adelaide

A discrete isometry group acting properly discontinuously on the n-dimensional Euclidean space with compact quotient is called a crystallographic group. This name reflects the fact that in dimension n=3 their compact fundamental domains resemble a space-filling crystal pattern. For higher dimensions, Hilbert posed his famous 18th problem: "Is there in n-dimensional Euclidean space only a finite number of essentially different kinds of groups of motions with a [compact] fundamental region?" This problem was solved by Bieberbach when he proved that in every dimension n there exists only a finite number of isomorphic crystallographic groups and also gave a description of these groups. From the perspective of differential geometry these results are of major importance, as crystallographic groups are precisely the fundamental groups of compact flat Riemannian orbifolds. The quotient is even a manifold if the fundamental group is required to be torsion-free, in which case it is called a Bieberbach group. Moreover, for a flat manifold the fundamental group completely determines the holonomy group. In this talk I will discuss the properties of crystallographic groups, study examples in dimension n=2 and n=3, and present the three Bieberbach theorems on the structure of crystallographic groups.
K-homology and the quantization commutes with reduction problem
12:10 Fri 5 Jul, 2013 :: 7.15 Ingkarni Wardli :: Prof Nigel Higson :: Pennsylvania State University

The quantization commutes with reduction problem for Hamiltonian actions of compact Lie groups was solved by Meinrenken in the mid-1990s using geometric techniques, and solved again shortly afterwards by Tian and Zhang using analytic methods. In this talk I shall outline some of the close links that exist between the problem, the two solutions, and the geometric and analytic versions of K-homology theory that are studied in noncommutative geometry. I shall try to make the case for K-homology as a useful conceptual framework for the solutions and (at least some of) their various generalizations.
Subfactors and twisted equivariant K-theory
12:10 Fri 2 Aug, 2013 :: Ingkarni Wardli B19 :: Prof David E. Evans :: Cardiff University

The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFTs associated to loop groups as twisted equivariant K-theory. In joint work with Terry Gannon, we build on their work to express K-theoretically the structures of full CFT. In particular, the modular invariant partition functions (which essentially parametrise the possible full CFTs) have a rich interpretation within von Neumann algebras (subfactors), which has led to the developments of structures of full CFT such as the full system (fusion ring of defect lines), nimrep (cylindrical partition function), alpha-induction etc.
The Einstein equations with torsion, reduction and duality
12:10 Fri 23 Aug, 2013 :: Ingkarni Wardli B19 :: Dr David Baraglia :: University of Adelaide

We consider the Einstein equations for connections with skew torsion. After some general remarks we look at these equations on principal G-bundles, making contact with string structures and heterotic string theory in the process. When G is a torus the equations are shown to possess a symmetry not shared by the usual Einstein equations - T-duality. This is joint work with Pedram Hekmati.
Noncommutative geometry and conformal geometry
13:10 Mon 16 Sep, 2013 :: Ingkarni Wardli B20 :: Prof Raphael Ponge :: Seoul National University

In this talk we shall report on a program of using the recent framework of twisted spectral triples to study conformal geometry from a noncommutative geometric perspective. One result is a local index formula in conformal geometry taking into account the action of the group of conformal diffeomorphisms. Another result is a version of Vafa-Witten's inequality for twisted spectral triples. Geometric applications include a version of Vafa-Witten's inequality in conformal geometry. There are also noncommutative versions for spectral triples over noncommutative tori and duals of discrete cocompact subgroups of semisimple Lie groups satisfying the Baum-Connes conjecture. (This is joint work with Hang Wang.)
Reductive group actions and some problems concerning their quotients
12:10 Fri 17 Jan, 2014 :: Ingkarni Wardli B20 :: Prof Gerald Schwarz :: Brandeis University

We will gently introduce the concept of a complex reductive group and the notion of the quotient Z of a complex vector space V on which our complex reductive group G acts linearly. There is the quotient mapping p from V to Z. The quotient is an affine variety with a stratification coming from the group action. Let f be an automorphism of Z. We consider the following questions (and give some answers). 1) Does f preserve the stratification of Z, i.e., does it permute the strata? 2) Is there a lift F of f? This means that F maps V to V and p(F(v))=f(p(v)) for all v in V. 3) Can we arrange that F is equivariant? We show that 1) is almost always true, that 2) is true in a lot of cases and that a twisted version of 3) then holds.
15:10 Fri 11 Apr, 2014 :: 5.58 Ingkarni Wardli :: Associate Professor John Middleton :: SARDI Aquatic Sciences and University of Adelaide

Aquaculture farming involves daily feeding of finfish and a subsequent excretion of nutrients into Spencer Gulf. Typically, finfish farming is done in six or so 50m diameter cages and over 600m X 600m lease sites. To help regulate the industry, it is desired that the finfish feed rates and the associated nutrient flux into the ocean are determined such that the maximum nutrient concentration c does not exceed a prescribed value (say cP) for ecosystem health. The prescribed value cP is determined by guidelines from the E.P.A. The concept is known as carrying capacity since limiting the feed rates limits the biomass of the farmed finfish. Here, we model the concentrations that arise from a constant input flux (F) of nutrients in a source region (the cage or lease) using the (depth-averaged) two dimensional, advection diffusion equation for constant and sinusoidal (tides) currents. Application of the divergence theorem to this equation results in a new scale estimate of the maximum flux F (and thus feed rate) that is given by F= cP /T* (1) where cP is the maximum allowed concentration and T* is a new time scale of “flushing” that involves both advection and diffusion. The scale estimate (1) is then shown to compare favourably with mathematically exact solutions of the advection diffusion equation that are obtained using Green’s functions and Fourier transforms. The maximum nutrient flux and associated feed rates are then estimated everywhere in Spencer Gulf through the development and validation of a hydrodynamic model. The model provides seasonal averages of the mean currents U and horizontal diffusivities KS that are needed to estimate T*. The diffusivities are estimated from a shear dispersal model of the tides which are very large in the gulf. The estimates have been provided to PIRSA Fisheries and Aquaculture to assist in the sustainable expansion of finfish aquaculture.
A generalised Kac-Peterson cocycle
11:10 Thu 17 Apr, 2014 :: Ingkarni Wardli B20 :: Pedram Hekmati :: University of Adelaide

The Kac-Peterson cocycle appears in the study of highest weight modules of infinite dimensional Lie algebras and determines a central extension. The vanishing of its cohomology class is tied to the existence of a cubic Dirac operator whose square is a quadratic Casimir element. I will introduce a closely related Lie algebra cocycle that comes about when constructing spin representations and gives rise to a Banach Lie group with a highly nontrivial topology. I will also explain how to make sense of the cubic Dirac operator in this setting and discuss its relation to twisted K-theory. This is joint work with Jouko Mickelsson.
The Bismut-Chern character as dimension reduction functor and its twisting
12:10 Fri 4 Jul, 2014 :: Ingkarni Wardli B20 :: Fei Han :: National University of Singapore

The Bismut-Chern character is a loop space refinement of the Chern character. It plays an essential role in the interpretation of the Atiyah-Singer index theorem from the point of view of loop space. In this talk, I will first briefly review the construction of the Bismut-Chern character and show how it can be viewed as a dimension reduction functor in the Stolz-Teichner program on supersymmetric quantum field theories. I will then introduce the construction of the twisted Bismut-Chern character, which represents our joint work with Varghese Mathai.
T-duality and the chiral de Rham complex
12:10 Fri 22 Aug, 2014 :: Ingkarni Wardli B20 :: Andrew Linshaw :: University of Denver

The chiral de Rham complex of Malikov, Schechtman, and Vaintrob is a sheaf of vertex algebras that exists on any smooth manifold M. It has a square-zero differential D, and contains the algebra of differential forms on M as a subcomplex. In this talk, I'll give an introduction to vertex algebras and sketch this construction. Finally, I'll discuss a notion of T-duality in this setting. This is based on joint work in progress with V. Mathai.
Spherical T-duality
01:10 Mon 25 Aug, 2014 :: Ingkarni Wardli B18 :: Mathai Varghese :: University of Adelaide

I will talk on a new variant of T-duality, called spherical T-duality, which relates pairs of the form (P,H) consisting of a principal SU(2)-bundle P --> M and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c_2(P). This is precisely true when M is compact oriented and dim(M) is at most 4. When M is higher dimensional, not all pairs (P,H) admit spherical T-duals and even when they exist, the spherical T-duals are not always unique. We will try and explain this phenomenon. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when dim(M) is at most 7, also their integral twisted cohomologies and, when dim(M) is at most 4, even their 7-twisted K-theories. While the complete physical relevance of spherical T-duality is still being explored, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications. This is joint work with Peter Bouwknegt and Jarah Evslin.
Ideal membership on singular varieties by means of residue currents
12:10 Fri 29 Aug, 2014 :: Ingkarni Wardli B20 :: Richard Larkang :: University of Adelaide

On a complex manifold X, one can consider the following ideal membership problem: Does a holomorphic function on X belong to a given ideal of holomorphic functions on X? Residue currents give a way of expressing analytically this essentially algebraic problem. I will discuss some basic cases of this, why such an analytic description might be useful, and finish by discussing a generalization of this to singular varieties.
Spectral asymptotics on random Sierpinski gaskets
12:10 Fri 26 Sep, 2014 :: Ingkarni Wardli B20 :: Uta Freiberg :: Universitaet Stuttgart

Self similar fractals are often used in modeling porous media. Hence, defining a Laplacian and a Brownian motion on such sets describes transport through such materials. However, the assumption of strict self similarity could be too restricting. So, we present several models of random fractals which could be used instead. After recalling the classical approaches of random homogenous and recursive random fractals, we show how to interpolate between these two model classes with the help of so called V-variable fractals. This concept (developed by Barnsley, Hutchinson & Stenflo) allows the definition of new families of random fractals, hereby the parameter V describes the degree of `variability' of the realizations. We discuss how the degree of variability influences the geometric, analytic and stochastic properties of these sets. - These results have been obtained with Ben Hambly (University of Oxford) and John Hutchinson (ANU Canberra).
The Serre-Grothendieck theorem by geometric means
12:10 Fri 24 Oct, 2014 :: Ingkarni Wardli B20 :: David Roberts :: University of Adelaide

The Serre-Grothendieck theorem implies that every torsion integral 3rd cohomology class on a finite CW-complex is the invariant of some projective bundle. It was originally proved in a letter by Serre, used homotopical methods, most notably a Postnikov decomposition of a certain classifying space with divisible homotopy groups. In this talk I will outline, using work of the algebraic geometer Offer Gabber, a proof for compact smooth manifolds using geometric means and a little K-theory.
Factorisations of Distributive Laws
12:10 Fri 19 Dec, 2014 :: Ingkarni Wardli B20 :: Paul Slevin :: University of Glasgow

Recently, distributive laws have been used by Boehm and Stefan to construct new examples of duplicial (paracyclic) objects, and hence cyclic homology theories. The paradigmatic example of such a theory is the cyclic homology HC(A) of an associative algebra A. It was observed by Kustermans, Murphy, and Tuset that the functor HC can be twisted by automorphisms of A. It turns out that this twisting procedure can be applied to any duplicial object defined by a distributive law. I will begin by defining duplicial objects and cyclic homology, as well as discussing some categorical concepts, then describe the construction of Boehm and Stefan. I will then define the category of factorisations of a distributive law and explain how this acts on their construction, and give some examples, making explicit how the action of this category generalises the twisting of an associative algebra.
On the analyticity of CR-diffeomorphisms
12:10 Fri 13 Mar, 2015 :: Engineering North N132 :: Ilya Kossivskiy :: University of Vienna

One of the fundamental objects in several complex variables is CR-mappings. CR-mappings naturally occur in complex analysis as boundary values of mappings between domains, and as restrictions of holomorphic mappings onto real submanifolds. It was already observed by Cartan that smooth CR-diffeomorphisms between CR-submanifolds in C^N tend to be very regular, i.e., they are restrictions of holomorphic maps. However, in general smooth CR-mappings form a more restrictive class of mappings. Thus, since the inception of CR-geometry, the following general question has been of fundamental importance for the field: Are CR-equivalent real-analytic CR-structures also equivalent holomorphically? In joint work with Lamel, we answer this question in the negative, in any positive CR-dimension and CR-codimension. Our construction is based on a recent dynamical technique in CR-geometry, developed in my earlier work with Shafikov.
Dirac operators and Hamiltonian loop group action
12:10 Fri 24 Jul, 2015 :: Engineering and Maths EM212 :: Yanli Song :: University of Toronto

A definition to the geometric quantization for compact Hamiltonian G-spaces is given by Bott, defined as the index of the Spinc-Dirac operator on the manifold. In this talk, I will explain how to generalize this idea to the Hamiltonian LG-spaces. Instead of quantizing infinite-dimensional manifolds directly, we use its equivalent finite-dimensional model, the quasi-Hamiltonian G-spaces. By constructing twisted spinor bundle and twisted pre-quantum bundle on the quasi-Hamiltonian G-space, we define a Dirac operator whose index are given by positive energy representation of loop groups. A key role in the construction will be played by the algebraic cubic Dirac operator for loop algebra. If time permitted, I will also explain how to prove the quantization commutes with reduction theorem for Hamiltonian LG-spaces under this framework.
Quantising proper actions on Spin-c manifolds
11:00 Fri 31 Jul, 2015 :: Ingkarni Wardli Level 7 Room 7.15 :: Peter Hochs :: The University of Adelaide

For a proper action by a Lie group on a Spin-c manifold (both of which may be noncompact), we study an index of deformations of the Spin-c Dirac operator, acting on the space of spinors invariant under the group action. When applied to spinors that are square integrable transversally to orbits in a suitable sense, the kernel of this operator turns out to be finite-dimensional, under certain hypotheses of the deformation. This also allows one to show that the index has the quantisation commutes with reduction property (as proved by Meinrenken in the compact symplectic case, and by Paradan-Vergne in the compact Spin-c case), for sufficiently large powers of the determinant line bundle. Furthermore, this result extends to Spin-c Dirac operators twisted by vector bundles. A key ingredient of the arguments is the use of a family of inner products on the Lie algebra, depending on a point in the manifold. This is joint work with Mathai Varghese.
Mathematical Modeling and Analysis of Active Suspensions
14:10 Mon 3 Aug, 2015 :: Napier 209 :: Professor Michael Shelley :: Courant Institute of Mathematical Sciences, New York University

Complex fluids that have a 'bio-active' microstructure, like suspensions of swimming bacteria or assemblies of immersed biopolymers and motor-proteins, are important examples of so-called active matter. These internally driven fluids can have strange mechanical properties, and show persistent activity-driven flows and self-organization. I will show how first-principles PDE models are derived through reciprocal coupling of the 'active stresses' generated by collective microscopic activity to the fluid's macroscopic flows. These PDEs have an interesting analytic structures and dynamics that agree qualitatively with experimental observations: they predict the transitions to flow instability and persistent mixing observed in bacterial suspensions, and for microtubule assemblies show the generation, propagation, and annihilation of disclination defects. I'll discuss how these models might be used to study yet more complex biophysical systems.
Analytic complexity of bivariate holomorphic functions and cluster trees
12:10 Fri 2 Oct, 2015 :: Ingkarni Wardli B17 :: Timur Sadykov :: Plekhanov University, Moscow

The Kolmogorov-Arnold theorem yields a representation of a multivariate continuous function in terms of a composition of functions which depend on at most two variables. In the analytic case, understanding the complexity of such a representation naturally leads to the notion of the analytic complexity of (a germ of) a bivariate multi-valued analytic function. According to Beloshapka's local definition, the order of complexity of any univariate function is equal to zero while the n-th complexity class is defined recursively to consist of functions of the form a(b(x,y)+c(x,y)), where a is a univariate analytic function and b and c belong to the (n-1)-th complexity class. Such a represenation is meant to be valid for suitable germs of multi-valued holomorphic functions. A randomly chosen bivariate analytic functions will most likely have infinite analytic complexity. However, for a number of important families of special functions of mathematical physics their complexity is finite and can be computed or estimated. Using this, we introduce the notion of the analytic complexity of a binary tree, in particular, a cluster tree, and investigate its properties.
Multi-scale modeling in biofluids and particle aggregation
15:10 Fri 17 Jun, 2016 :: B17 Ingkarni Wardli :: Dr Sarthok Sircar :: University of Adelaide

In today's seminar I will give 2 examples in mathematical biology which describes the multi-scale organization at 2 levels: the meso/micro level and the continuum/macro level. I will then detail suitable tools in statistical mechanics to link these different scales. The first problem arises in mathematical physiology: swelling-de-swelling mechanism of mucus, an ionic gel. Mucus is packaged inside cells at high concentration (volume fraction) and when released into the extracellular environment, it expands in volume by two orders of magnitude in a matter of seconds. This rapid expansion is due to the rapid exchange of calcium and sodium that changes the cross-linked structure of the mucus polymers, thereby causing it to swell. Modeling this problem involves a two-phase, polymer/solvent mixture theory (in the continuum level description), together with the chemistry of the polymer, its nearest neighbor interaction and its binding with the dissolved ionic species (in the micro-scale description). The problem is posed as a free-boundary problem, with the boundary conditions derived from a combination of variational principle and perturbation analysis. The dynamics of neutral gels and the equilibrium-states of the ionic gels are analyzed. In the second example, we numerically study the adhesion fragmentation dynamics of rigid, round particles clusters subject to a homogeneous shear flow. In the macro level we describe the dynamics of the number density of these cluster. The description in the micro-scale includes (a) binding/unbinding of the bonds attached on the particle surface, (b) bond torsion, (c) surface potential due to ionic medium, and (d) flow hydrodynamics due to shear flow.
Twists over etale groupoids and twisted vector bundles
12:10 Fri 22 Jul, 2016 :: Ingkarni Wardli B18 :: Elizabeth Gillaspy :: University of Colorado, Boulder

Given a twist over an etale groupoid, one can construct an associated C*-algebra which carries a good deal of geometric and physical meaning; for example, the K-theory group of this C*-algebra classifies D-brane charges in string theory. Twisted vector bundles, when they exist, give rise to particularly important elements in this K-theory group. In this talk, we will explain how to use the classifying space of the etale groupoid to construct twisted vector bundles, under some mild hypotheses on the twist and the classifying space. My hope is that this talk will be accessible to a broad audience; in particular, no prior familiarity with groupoids, their twists, or the associated C*-algebras will be assumed. This is joint work with Carla Farsi.
Holomorphic Flexibility Properties of Spaces of Elliptic Functions
12:10 Fri 29 Jul, 2016 :: Ingkarni Wardli B18 :: David Bowman :: University of Adelaide

The set of meromorphic functions on an elliptic curve naturally possesses the structure of a complex manifold. The component of degree 3 functions is 6-dimensional and enjoys several interesting complex-analytic properties that make it, loosely speaking, the opposite of a hyperbolic manifold. Our main result is that this component has a 54-sheeted branched covering space that is an Oka manifold.
Calculus on symplectic manifolds
12:10 Fri 12 Aug, 2016 :: Ingkarni Wardli B18 :: Mike Eastwood :: University of Adelaide

One can use the symplectic form to construct an elliptic complex replacing the de Rham complex. Then, under suitable curvature conditions, one can form coupled versions of this complex. Finally, on complex projective space, these constructions give rise to a series of elliptic complexes with geometric consequences for the Fubini-Study metric and its X-ray transform. This talk, which will start from scratch, is based on the work of many authors but, especially, current joint work with Jan Slovak.
SIR epidemics with stages of infection
12:10 Wed 28 Sep, 2016 :: EM218 :: Matthieu Simon :: Universite Libre de Bruxelles

This talk is concerned with a stochastic model for the spread of an epidemic in a closed homogeneously mixing population. The population is subdivided into three classes of individuals: the susceptibles, the infectives and the removed cases. In short, an infective remains infectious during a random period of time. While infected, it can contact all the susceptibles present, independently of the other infectives. At the end of the infectious period, it becomes a removed case and has no further part in the infection process.

We represent an infectious period as a set of different stages that an infective can go through before being removed. The transitions between stages are ruled by either a Markov process or a semi-Markov process. In each stage, an infective makes contaminations at the epochs of a Poisson process with a specific rate.

Our purpose is to derive closed expressions for a transform of different statistics related to the end of the epidemic, such as the final number of susceptibles and the area under the trajectories of all the infectives. The analysis is performed by using simple matrix analytic methods and martingale arguments. Numerical illustrations will be provided at the end of the talk.
Diffeomorphisms of discs, harmonic spinors and positive scalar curvature
11:10 Fri 17 Mar, 2017 :: Engineering Nth N218 :: Diarmuid Crowley :: University of Melbourne

Let Diff(D^k) be the space of diffeomorphisms of the k-disc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have non-zero 8-periodic 2-torsion detected in real K-theory. I will then discuss applications for spin manifolds M of dimension 6 or greater: 1) Our results input to arguments of Hitchin which now show that M admits a metric with a harmonic spinor. 2) If non-empty, space of positive scalar curvature metrics on M has non-zero 8-periodic 2-torsion in its homotopy groups which is detected in real K-theory. This is part of joint work with Thomas Schick and Wolfgang Steimle.
What is index theory?
12:10 Tue 21 Mar, 2017 :: Inkgarni Wardli 5.57 :: Dr Peter Hochs :: School of Mathematical Sciences

Index theory is a link between topology, geometry and analysis. A typical theorem in index theory says that two numbers are equal: an analytic index and a topological index. The first theorem of this kind was the index theorem of Atiyah and Singer, which they proved in 1963. Index theorems have many applications in maths and physics. For example, they can be used to prove that a differential equation must have a solution. Also, they imply that the topology of a space like a sphere or a torus determines in what ways it can be curved. Topology is the study of geometric properties that do not change if we stretch or compress a shape without cutting or glueing. Curvature does change when we stretch something out, so it is surprising that topology can say anything about curvature. Index theory has many surprising consequences like this.
Real bundle gerbes
12:10 Fri 19 May, 2017 :: Napier 209 :: Michael Murray :: University of Adelaide

Bundle gerbe modules, via the notion of bundle gerbe K-theory provide a realisation of twisted K-theory. I will discuss the existence or Real bundle gerbes which are the corresponding objects required to construct Real twisted K-theory in the sense of Atiyah. This is joint work with Richard Szabo (Heriot-Watt), Pedram Hekmati (Auckland) and Raymond Vozzo which appeared in arXiv:1608.06466.
Stokes' Phenomenon in Translating Bubbles
15:10 Fri 2 Jun, 2017 :: Ingkarni Wardli 5.57 :: Dr Chris Lustri :: Macquarie University

This study of translating air bubbles in a Hele-Shaw cell containing viscous fluid reveals the critical role played by surface tension in these systems. The standard zero-surface-tension model of Hele-Shaw flow predicts that a continuum of bubble solutions exists for arbitrary flow translation velocity. The inclusion of small surface tension, however, eliminates this continuum of solutions, instead producing a discrete, countably infinite family of solutions, each with distinct translation speeds. We are interested in determining this discrete family of solutions, and understanding why only these solutions are permitted. Studying this problem in the asymptotic limit of small surface tension does not seem to give any particular reason why only these solutions should be selected. It is only by using exponential asymptotic methods to study the Stokes’ structure hidden in the problem that we are able to obtain a complete picture of the bubble behaviour, and hence understand the selection mechanism that only permits certain solutions to exist. In the first half of my talk, I will explain the powerful ideas that underpin exponential asymptotic techniques, such as analytic continuation and optimal truncation. I will show how they are able to capture behaviour known as Stokes' Phenomenon, which is typically invisible to classical asymptotic series methods. In the second half of the talk, I will introduce the problem of a translating air bubble in a Hele-Shaw cell, and show that the behaviour can be fully understood by examining the Stokes' structure concealed within the problem. Finally, I will briefly showcase other important physical applications of exponential asymptotic methods, including submarine waves and particle chains.
Constructing differential string structures
14:10 Wed 7 Jun, 2017 :: EM213 :: David Roberts :: University of Adelaide

String structures on a manifold are analogous to spin structures, except instead of lifting the structure group through the extension Spin(n)\to SO(n) of Lie groups, we need to lift through the extension String(n)\to Spin(n) of Lie *2-groups*. Such a thing exists if the first fractional Pontryagin class (1/2)p_1 vanishes in cohomology. A differential string structure also lifts connection data, but this is rather complicated, involving a number of locally defined differential forms satisfying cocycle-like conditions. This is an expansion of the geometric string structures of Stolz and Redden, which is, for a given connection A, merely a 3-form R on the frame bundle such that dR = tr(F^2) for F the curvature of A; in other words a trivialisation of the de Rham class of (1/2)p_1. I will present work in progress on a framework (and specific results) that allows explicit calculation of the differential string structure for a large class of homogeneous spaces, which also yields formulas for the Stolz-Redden form. I will comment on the application to verifying the refined Stolz conjecture for our particular class of homogeneous spaces. Joint work with Ray Vozzo.
Time-reversal symmetric topology from physics
12:10 Fri 25 Aug, 2017 :: Engineering Sth S111 :: Guo Chuan Thiang :: University of Adelaide

Time-reversal plays a crucial role in experimentally discovered topological insulators (2008) and semimetals (2015). This is mathematically interesting because one is forced to use "Quaternionic" characteristic classes and differential topology --- a previously ill-motivated generalisation. Guided by physical intuition, an equivariant Poincare-Lefschetz duality, Euler structures, and a new type of monopole with torsion charge, will be introduced.
How oligomerisation impacts steady state gradient in a morphogen-receptor system
15:10 Fri 20 Oct, 2017 :: Ingkarni Wardli 5.57 :: Mr Phillip Brown :: University of Adelaide

In developmental biology an important process is cell fate determination, where cells start to differentiate their form and function. This is an element of the broader concept of morphogenesis. It has long been held that cell differentiation can occur by a chemical signal providing positional information to 'undecided' cells. This chemical produces a gradient of concentration that indicates to a cell what path it should develop along. More recently it has been shown that in a particular system of this type, the chemical (protein) does not exist purely as individual molecules, but can exist in multi-protein complexes known as oligomers. Mathematical modelling has been performed on systems of oligomers to determine if this concept can produce useful gradients of concentration. However, there are wide range of possibilities when it comes to how oligomer systems can be modelled and most of them have not been explored. In this talk I will introduce a new monomer system and analyse it, before extending this model to include oligomers. A number of oligomer models are proposed based on the assumption that proteins are only produced in their oligomer form and can only break apart once they have left the producing cell. It will be shown that when oligomers are present under these conditions, but only monomers are permitted to bind with receptors, then the system can produce robust, biologically useful gradients for a significantly larger range of model parameters (for instance, degradation, production and binding rates) compared to the monomer system. We will also show that when oligomers are permitted to bind with receptors there is negligible difference compared to the monomer system.
The topology and geometry of spaces of Yang-Mills-Higgs flow lines
11:10 Fri 27 Jul, 2018 :: Barr Smith South Polygon Lecture theatre :: Graeme Wilkin :: National University of Singapore

Given a smooth complex vector bundle over a compact Riemann surface, one can define the space of Higgs bundles and an energy functional on this space: the Yang-Mills-Higgs functional. The gradient flow of this functional resembles a nonlinear heat equation, and the limit of the flow detects information about the algebraic structure of the initial Higgs bundle (e.g. whether or not it is semistable). In this talk I will explain my work to classify ancient solutions of the Yang-Mills-Higgs flow in terms of their algebraic structure, which leads to an algebro-geometric classification of Yang-Mills-Higgs flow lines. Critical points connected by flow lines can then be interpreted in terms of the Hecke correspondence, which appears in Witten’s recent work on Geometric Langlands. This classification also gives a geometric description of spaces of unbroken flow lines in terms of secant varieties of the underlying Riemann surface, and in the remaining time I will describe work in progress to relate the (analytic) Morse compactification of these spaces by broken flow lines to an algebro-geometric compactification by iterated blowups of secant varieties.
Min-max theory for hypersurfaces of prescribed mean curvature
11:10 Fri 17 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Jonathan Zhu :: Harvard University

We describe the construction of closed prescribed mean curvature (PMC) hypersurfaces using min-max methods. Our theory allows us to show the existence of closed PMC hypersurfaces in a given closed Riemannian manifold for a generic set of ambient prescription functions. This set includes, in particular, all constant functions as well as analytic functions if the manifold is real analytic. The described work is joint with Xin Zhou.
Twisted K-theory of compact Lie groups and extended Verlinde algebras
11:10 Fri 12 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Chi-Kwong Fok :: University of Adelaide

In a series of recent papers, Freed, Hopkins and Teleman put forth a deep result which identifies the twisted K -theory of a compact Lie group G with the representation theory of its loop group LG. Under suitable conditions, both objects can be enhanced to the Verlinde algebra, which appears in mathematical physics as the Frobenius algebra of a certain topological quantum field theory, and in algebraic geometry as the algebra encoding information of moduli spaces of G-bundles over Riemann surfaces. The Verlinde algebra for G with nice connectedness properties have been well-known. However, explicit descriptions of such for disconnected G are lacking. In this talk, I will discuss the various aspects of the Freed-Hopkins-Teleman Theorem and partial results on an extension of the Verlinde algebra arising from a disconnected G. The talk is based on work in progress joint with David Baraglia and Varghese Mathai.
How long does it take to get there?
11:10 Fri 19 Oct, 2018 :: Engineering North N132 :: Professor Herbert Huppert :: University of Cambridge

In many situations involving nonlinear partial differential equations, requiring much numerical calculation because there is no analytic solution, it is possible to find a similarity solution to the resulting (still nonlinear) ordinary differential equation; sometimes even analytically, but it is generally independent of the initial conditions. The similarity solution is said to approach the real solution for t >> tau, say. But what is tau? How does it depend on the parameters of the problem and the initial conditions? Answers will be presented for a variety of problems and the audience will be asked to suggest others if they know of them.

News matching "Analytic torsion for twisted de Rham complexes"

ARC Grant successes
The School of Mathematical Sciences has again had outstanding success in the ARC Discovery and Linkage Projects schemes. Congratulations to the following staff for their success in the Discovery Project scheme: Prof Nigel Bean, Dr Josh Ross, Prof Phil Pollett, Prof Peter Taylor, New methods for improving active adaptive management in biological systems, $255,000 over 3 years; Dr Josh Ross, New methods for integrating population structure and stochasticity into models of disease dynamics, $248,000 over three years; A/Prof Matt Roughan, Dr Walter Willinger, Internet traffic-matrix synthesis, $290,000 over three years; Prof Patricia Solomon, A/Prof John Moran, Statistical methods for the analysis of critical care data, with application to the Australian and New Zealand Intensive Care Database, $310,000 over 3 years; Prof Mathai Varghese, Prof Peter Bouwknegt, Supersymmetric quantum field theory, topology and duality, $375,000 over 3 years; Prof Peter Taylor, Prof Nigel Bean, Dr Sophie Hautphenne, Dr Mark Fackrell, Dr Malgorzata O'Reilly, Prof Guy Latouche, Advanced matrix-analytic methods with applications, $600,000 over 3 years. Congratulations to the following staff for their success in the Linkage Project scheme: Prof Simon Beecham, Prof Lee White, A/Prof John Boland, Prof Phil Howlett, Dr Yvonne Stokes, Mr John Wells, Paving the way: an experimental approach to the mathematical modelling and design of permeable pavements, $370,000 over 3 years; Dr Amie Albrecht, Prof Phil Howlett, Dr Andrew Metcalfe, Dr Peter Pudney, Prof Roderick Smith, Saving energy on trains - demonstration, evaluation, integration, $540,000 over 3 years Posted Fri 29 Oct 10.

Publications matching "Analytic torsion for twisted de Rham complexes"

Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls
Larusson, Finnur; Sigurdsson, R, Mathematische Annalen 345 (159–174) 2009
Learning fuzzy rules with evolutionary algorithms - An analytic approach
Kroeske, Jens; Ghandar, Adam; Michalewicz, Zbigniew; Neumann, F, 10th International Conference on Parallel Problem Solving from Nature, Germany 01/09/08
Oriented bond percolation and phase transitions: an analytic approach
Pearce, Charles, International Conference on Numerical Analysis and Applied Mathematics, Corfu, Greece 16/09/07
Fractional analytic index
Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 74 (265–292) 2006
Heat kernels and the range of the trace on completions of twisted group algebras
Varghese, Mathai, Contemporary Mathematics 398 (321–345) 2006
Mathematical modelling of oxygen concentration in bovine and murine cumulus-oocyte complexes
Clark, Alys; Stokes, Yvonne; Lane, Michelle; Thompson, Jeremy, Reproduction 131 (999–1006) 2006
Methodology in meta-analysis: a study from critical care meta-analytic practice
Moran, John; Solomon, Patricia; Warn, D, Health Services and Outcomes Research Methodology 5 (207–226) 2006
An analytic modelling approach for network routing algorithms that use "ant-like" mobile agents
Bean, Nigel; Costa, Andre, Computer Networks-The International Journal of Computer and Telecommunications Networking 49 (243–268) 2005
L2 torsion without the determinant class condition and extended L2 cohomology
Braverman, M; Carey, Alan; Farber, M; Varghese, Mathai, Communications in Contemporary Mathematics 7 (421–462) 2005
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
Second moments of a matrix analytic model of machine maintenance
Green, David; Metcalfe, Andrew, IMA International Conference on Modelling in Industrial Maintenance and Reliability (5th: 2004), Salford, United Kingdom 05/04/04
Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible
Roberts, Anthony John, SIAM Journal on Applied Dynamical Systems 3 (433–462) 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
Chern character in twisted K-theory: Equivariant and holomorphic cases
Varghese, Mathai; Stevenson, Daniel, Communications in Mathematical Physics 236 (161–186) 2003
Edge of the wedge theory in hypo-analytic manifolds
Eastwood, Michael; Graham, C, Communications in Partial Differential Equations 28 (2003–2028) 2003
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
Nonclassical description of analytic cohomology
Bailey, T; Eastwood, Michael; Gindikin, S,
A matrix analytic model for machine maintenance
Green, David; Metcalfe, Andrew; Swailes, D, Matrix-Analytic Methods: Theory and Applications, Adelaide, Australia 14/07/02
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
Flow in spiral channels of small curvature and torsion
Stokes, Yvonne, The IUTAM Symposium on Free Surface Flows, Birmingham, UK 10/07/00
Twisted index theory on good orbifolds, II: Fractional quantum numbers
Marcolli, M; Varghese, Mathai, Communications in Mathematical Physics 217 (55–87) 2001
Analytic continuation of vector bundles with Lp-curvature
Harris, A; Tonegawa, Y, International Journal of Mathematics 11 (29–40) 2000
Correspondences, von Neumann algebras and holomorphic L2 torsion
Carey, Alan; Farber, M; Varghese, Mathai, Canadian Journal of Mathematics-Journal Canadien de Mathematiques 52 (695–736) 2000
D-Branes, B-Fields and twisted K-theory
Bouwknegt, Pier; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (1–11) 2000

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