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August 2019

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Events matching "Spherical T-duality"

The Mathematics of String Theory
15:10 Fri 2 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Peter Bouwknegt :: Department of Mathematics, ANU

String Theory has had, and continues to have, a profound impact on many areas of mathematics and vice versa. In this talk I want to address some relatively recent developments. In particular I will argue, following Witten and others, that D-brane charges take values in the K-theory of spacetime, rather than in integral cohomology as one might have expected. I will also explore the mathematical consequences of a particular symmetry, called T-duality, in this context. I will give an intuitive introduction into D-branes and K-theory. No prior knowledge about either String Theory, D-branes or K-theory is required.
Impulsively generated drops
15:00 Fri 27 Feb, 2009 :: Napier LG29 :: Prof William Phillips :: Swinburne University of Technology

This talk is concerned with the evolution of an unbounded inviscid fluid-fluid interface subject to an axisymmetric impulse in pressure and how inertial, interfacial and gravitational forces affect that evolution. The construct was motivated by the occurrence of lung hemorrhage resulting from ultrasonic imaging and pursues the notion that bursts of ultrasound act to expel droplets that puncture the soft air-filled sacs in the lung plural surface allowing them to fill with blood. The evolution of the free surface is described by a boundary integral formulation which is integrated forward in time numerically. As the interface evolves, it is seen, depending upon the levels of gravity and surface tension, to form either axisymmetric surface jets, waves or droplets. Moreover the droplets may be spherical, inverted tear-shaped or pancake like. Also of interest is the finite time singularity which occurs when the drop pinches off; this is seen to be of the power law type with an exponent of 2/3.
Principal Component Analysis Revisited
15:10 Fri 15 Oct, 2010 :: Napier G04 :: Assoc. Prof Inge Koch :: University of Adelaide

Since the beginning of the 20th century, Principal Component Analysis (PCA) has been an important tool in the analysis of multivariate data. The principal components summarise data in fewer than the original number of variables without losing essential information, and thus allow a split of the data into signal and noise components. PCA is a linear method, based on elegant mathematical theory. The increasing complexity of data together with the emergence of fast computers in the later parts of the 20th century has led to a renaissance of PCA. The growing numbers of variables (in particular, high-dimensional low sample size problems), non-Gaussian data, and functional data (where the data are curves) are posing exciting challenges to statisticians, and have resulted in new research which extends the classical theory. I begin with the classical PCA methodology and illustrate the challenges presented by the complex data that we are now able to collect. The main part of the talk focuses on extensions of PCA: the duality of PCA and the Principal Coordinates of Multidimensional Scaling, Sparse PCA, and consistency results relating to principal components, as the dimension grows. We will also look at newer developments such as Principal Component Regression and Supervised PCA, nonlinear PCA and Functional PCA.
Spherical tube hypersurfaces
13:10 Fri 8 Apr, 2011 :: Mawson 208 :: Prof Alexander Isaev :: Australian National University

We consider smooth real hypersurfaces in a complex vector space. Specifically, we are interested in tube hypersurfaces, i.e., hypersurfaces represented as the direct product of the imaginary part of the space and hypersurfaces lying in its real part. Tube hypersurfaces arise, for instance, as the boundaries of tube domains. The study of tube domains is a classical subject in several complex variables and complex geometry, which goes back to the beginning of the 20th century. Indeed, already Siegel found it convenient to realise certain symmetric domains as tubes. One can endow a tube hypersurface with a so-called CR-structure, which is the remnant of the complex structure on the ambient vector space. We impose on the CR-structure the condition of sphericity. One way to state this condition is to require a certain curvature (called the CR-curvature of the hypersurface) to vanish identically. Spherical tube hypersurfaces possess remarkable properties and are of interest from both the complex-geometric and affine-geometric points of view. I my talk I will give an overview of the theory of such hypersurfaces. In particular, I will mention an algebraic construction arising from this theory that has applications in abstract commutative algebra and singularity theory. I will speak about these applications in detail in my colloquium talk later today.
T-duality via bundle gerbes I
13:10 Fri 23 Sep, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the H-flux). In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.
T-duality via bundle gerbes II
13:10 Fri 21 Oct, 2011 :: B.19 Ingkarni Wardli :: Dr Raymond Vozzo :: University of Adelaide

In physics T-duality is a phenomenon which relates certain types of string theories to one another. From a topological point of view, one can view string theory as a duality between line bundles carrying a degree three cohomology class (the H-flux). In this talk we will use bundle gerbes to give a geometric realisation of the H-flux and explain how to construct the T-dual of a line bundle together with its T-dual bundle gerbe.
Boundary-layer transition and separation over asymmetrically textured spherical surfaces
12:30 Mon 27 Aug, 2012 :: B.21 Ingkarni Wardli :: Mr Adam Tunney :: University of Adelaide

The game of cricket is unique among ball sports by the ignorant exploitation of \thetitle in the practice of swing bowling, often referred to as a "mysterious art". I will talk a bit about the Magnus effect exploited in inferior sports, the properties of a cricket ball that allow swing bowling, and the explanation of three modes of swing (conventional, contrast and reverse). Following that there will be some discussion on how I plan to use mathematics to turn this "art" into science.
Holomorphic flexibility properties of compact complex surfaces
13:10 Fri 31 Aug, 2012 :: Engineering North 218 :: A/Prof Finnur Larusson :: University of Adelaide

I will describe recent joint work with Franc Forstneric (arXiv, July 2012). We introduce a new property, called the stratified Oka property, which fits into a hierarchy of anti-hyperbolicity properties that includes the Oka property. We show that stratified Oka manifolds are strongly dominable by affine spaces. It follows that Kummer surfaces are strongly dominable. We determine which minimal surfaces of class VII are Oka (assuming the global spherical shell conjecture). We deduce that the Oka property and several other anti-hyperbolicity properties are in general not closed in families of compact complex manifolds. I will summarise what is known about how the Oka property fits into the Enriques-Kodaira classification of surfaces.
The advection-diffusion-reaction equation on the surface of the sphere
12:10 Mon 24 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr Kale Davies :: University of Adelaide

We aim to solve the advection-diffusion-reaction equation on the surface of a sphere. In order to do this we will be required to utilise spherical harmonics, a set of solutions to Laplace's equation in spherical coordinates. Upon solving the equations, we aim to find a set of parameters that cause a localised concentration to be maintained in the flow, referred to as a hotspot. In this talk I will discuss the techniques that are required to numerically solve this problem and the issues that occur/how to deal with these issues when searching for hotspot solutions.
Electrokinetics of concentrated suspensions of spherical particles
15:10 Fri 28 Sep, 2012 :: B.21 Ingkarni Wardli :: Dr Bronwyn Bradshaw-Hajek :: University of South Australia

Electrokinetic techniques are used to gather specific information about concentrated dispersions such as electronic inks, mineral processing slurries, pharmaceutical products and biological fluids (e.g. blood). But, like most experimental techniques, intermediate quantities are measured, and consequently the method relies explicitly on theoretical modelling to extract the quantities of experimental interest. A self-consistent cell-model theory of electrokinetics can be used to determine the electrical conductivity of a dense suspension of spherical colloidal particles, and thereby determine the quantities of interest (such as the particle surface potential). The numerical predictions of this model compare well with published experimental results. High frequency asymptotic analysis of the cell-model leads to some interesting conclusions.
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.
T-Duality and its Generalizations
12:10 Fri 11 Apr, 2014 :: Ingkarni Wardli B20 :: Jarah Evslin :: Theoretical Physics Center for Science Facilities, CAS

Given a manifold M with a torus action and a choice of integral 3-cocycle H, T-duality yields another manifold with a torus action and integral 3-cocyle. It induces a number of surprising automorphisms between structures on these manifolds. In this talk I will review T-duality and describe some work on two generalizations which are realized in string theory: NS5-branes and heterotic strings. These respectively correspond to non-closed 3-classes H and to principal bundles fibered over M.
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.
Tannaka duality for stacks
12:10 Fri 6 Mar, 2015 :: Ingkarni Wardli B20 :: Jack Hall :: Australian National University

Traditionally, Tannaka duality is used to reconstruct a group from its representations. I will describe a reformulation of this duality for stacks, which is due to Lurie, and briefly touch on some applications.
Spherical T-duality: the non-principal case
12:10 Fri 1 May, 2015 :: Napier 144 :: Mathai Varghese :: University of Adelaide

Spherical T-duality is related to M-theory and was introduced in recent joint work with Bouwknegt and Evslin. I will begin by briefly reviewing the case of principal SU(2)-bundles with degree 7 flux, and then focus on the non-principal case for most of the talk, ending with the relation to SUGRA/M-theory.
An Engineer-Mathematician Duality Approach to Finite Element Methods
12:10 Mon 18 May, 2015 :: Napier LG29 :: Jordan Belperio :: University of Adelaide

The finite element method has been a prominently used numerical technique for engineers solving solid mechanics, electro-magnetic and heat transfer problems for over 30 years. More recently the finite element method has been used to solve fluid mechanics problems, a field where finite difference methods are more commonly used. In this talk, I will introduce the basic mathematics behind the finite element method, the similarity between the finite element method and finite difference method and comparing how engineers and mathematicians use finite element methods. I will then demonstrate two solutions to the wave equation using the finite element method.
T-duality and bulk-boundary correspondence
12:10 Fri 11 Sep, 2015 :: Ingkarni Wardli B17 :: Guo Chuan Thiang :: The University of Adelaide

Bulk-boundary correspondences in physics can be modelled as topological boundary homomorphisms in K-theory, associated to an extension of a "bulk algebra" by a "boundary algebra". In joint work with V. Mathai, such bulk-boundary maps are shown to T-dualize into simple restriction maps in a large number of cases, generalizing what the Fourier transform does for ordinary functions. I will give examples, involving both complex and real K-theory, and explain how these results may be used to study topological phases of matter and D-brane charges in string theory.
T-duality for elliptic curve orientifolds
12:10 Fri 4 Mar, 2016 :: Ingkarni Wardli B17 :: Jonathan Rosenberg :: University of Maryland

Orientifold string theories are quantum field theories based on the geometry of a space with an involution. T-dualities are certain relationships between such theories that look different on the surface but give rise to the same observable physics. In this talk I will not assume any knowledge of physics but will concentrate on the associated geometry, in the case where the underlying space is a (complex) elliptic curve and the involution is either holomorphic or anti-holomorphic. The results blend algebraic topology and algebraic geometry. This is mostly joint work with Chuck Doran and Stefan Mendez-Diez.
Toroidal Soap Bubbles: Constant Mean Curvature Tori in S ^ 3 and R ^3
12:10 Fri 28 Oct, 2016 :: Ingkarni Wardli B18 :: Emma Carberry :: University of Sydney

Constant mean curvature (CMC) tori in S ^ 3, R ^ 3 or H ^ 3 are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the relevant space form. This point of view is particularly relevant for considering moduli-space questions, such as the prevalence of tori amongst CMC planes and whether tori can be deformed. I will address these questions for the spherical and Euclidean cases, using Whitham deformations.
Poisson-Lie T-duality and integrability
11:10 Thu 13 Apr, 2017 :: Engineering & Math EM213 :: Ctirad Klimcik :: Aix-Marseille University, Marseille

The Poisson-Lie T-duality relates sigma-models with target spaces symmetric with respect to mutually dual Poisson-Lie groups. In the special case if the Poisson-Lie symmetry reduces to the standard non-Abelian symmetry one of the corresponding mutually dual sigma-models is the standard principal chiral model which is known to enjoy the property of integrability. A natural question whether this non-Abelian integrability can be lifted to integrability of sigma model dualizable with respect to the general Poisson-Lie symmetry has been answered in the affirmative by myself in 2008. The corresponding Poisson-Lie symmetric and integrable model is a one-parameter deformation of the principal chiral model and features a remarkable explicit appearance of the standard Yang-Baxter operator in the target space geometry. Several distinct integrable deformations of the Yang-Baxter sigma model have been then subsequently uncovered which turn out to be related by the Poisson-Lie T-duality to the so called lambda-deformed sigma models. My talk gives a review of these developments some of which found applications in string theory in the framework of the AdS/CFT correspondence.
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.
Discrete fluxes and duality in gauge theory
11:10 Fri 24 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Siye Wu :: National Tsinghua University

We explore the notions of discrete electric and magnetic fluxes introduced by 't Hooft in the late 1970s. After explaining their physics origin, we consider the description in mathematical terminology. We finally study their role in duality.

News matching "Spherical T-duality"

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 "Spherical T-duality"

Non-commutative correspondences, duality and D-branes in bivariant K-theory
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Advances in Theoretical and Mathematical Physics 13 (497–552) 2009
T-duality as a duality of loop group bundles
Bouwknegt, Pier; Varghese, Mathai, Journal of Physics A: Mathematical and Theoretical (Print Edition) 42 (162001-1–162001-8) 2009
D-branes, KK-theory and duality on noncommutative spaces
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Journal of Physics: Conference Series (Print Edition) 103 (1–13) 2008
D-branes, RR-fields and duality on noncommutative manifolds
Brodzki, J; Varghese, Mathai; Rosenberg, J; Szabo, R, Communications in Mathematical Physics 277 (643–706) 2008
T-Duality in type II string theory via noncommutative geometry and beyond
Varghese, Mathai, Progress of Theoretical Physics Supplement 171 (237–257) 2007
On mysteriously missing T-duals, H-flux and the T-duality Group
Varghese, Mathai; Rosenberg, J, chapter in Differential geometry and physics (World Scientific Publishing) 350–358, 2006
Duality symmetry and the form fields of M-theory
Sati, Hicham, The Journal of High Energy Physics (Print Edition) 6 (0–10) 2006
Flux compactifications on projective spaces and the S-duality puzzle
Bouwknegt, Pier; Evslin, J; Jurco, B; Varghese, Mathai; Sati, Hicham, Advances in Theoretical and Mathematical Physics 10 (345–394) 2006
Nonassociative Tori and Applications to T-Duality
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Communications in Mathematical Physics 264 (41–69) 2006
T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
Varghese, Mathai; Rosenberg, J, Advances in Theoretical and Mathematical Physics 10 (123–158) 2006
Ramaswami's duality and probabilistic algorithms for determining the rate matrix for a structured GI/M/1 Markov chain
Hunt, Emma, The ANZIAM Journal 46 (485–493) 2005
T-duality for principal torus bundles and dimensionally reduced Gysin sequences
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, Advances in Theoretical and Mathematical Physics 9 (1–25) 2005
T-duality for torus bundles with H-fluxes via noncommutative topology
Varghese, Mathai; Rosenberg, J, Communications in Mathematical Physics 253 (705–721) 2005
Type IIB string theory, S-duality, and generalized cohomology
Kriz, I; Sati, Hicham, Nuclear Physics B 715 (639–664) 2005
T-duality for principal torus bundles
Bouwknegt, Pier; Hannabuss, K; Varghese, Mathai, The Journal of High Energy Physics (Online Editions) 3 (WWW 1–WWW 10) 2004
T-duality: Topology change from H-flux
Bouwknegt, Pier; Evslin, J; Varghese, Mathai, Communications in Mathematical Physics 249 (383–415) 2004
Topological duality in humanoid robot dynamics
Ivancevic, V; Pearce, Charles, The ANZIAM Journal 43 (183–194) 2001

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