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Search the School of Mathematical SciencesCourses matching "Introduction to pairings in cryptography" 
Introduction to Financial Mathematics I Algebra: Matrices and linear equations. Optimisation problems: solutions by graphical and algebraic methods.
Functions and Annuities: linear, quadratic, exponential and logarithmic functions; simple and compound interest, annuities and amortization of loans. Continuous rates of change and the derivative.
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Events matching "Introduction to pairings in cryptography" 
Finite Geometries: Classical Problems and Recent Developments 15:10 Fri 20 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Joseph A. Thas :: Ghent University, Belgium
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 GÃ¡cs, 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. 

An Introduction to invariant differential pairings 14:10 Tue 24 Jul, 2007 :: Mathematics G08 :: Jens Kroeske
On homogeneous spaces G/P, where G is a semisimple Lie group and P is a
parabolic subgroup (the ordinary sphere or projective spaces being
examples), invariant operators, that is operators between certain
homogeneous bundles (functions, vector fields or forms being amongst the
typical examples) that are invariant under the action of the group G, have
been studied extensively. Especially on so called hermitian symmetric spaces
which arise through a 1grading of the Lie algebra of G there exists a
complete classification of first order invariant linear differential
operators even on more general manifolds (that allow a so called almost
hermitian structure).
This talk will introduce the notion of an invariant bilinear differential
pairing between sections of the aforementioned homogeneous bundles. Moreover
we will discuss a classification (excluding certain totally degenerate
cases) of all first order invariant bilinear differential pairings on
manifolds with an almost hermitian symmetric structure. The similarities and
connections with the linear operator classification will be highlighted and
discussed.


Likelihood inference for a problem in particle physics 15:10 Fri 27 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Anthony Davison
The Large Hadron Collider (LHC), a particle accelerator located at CERN, near Geneva, is (currently!) expected to start operation in early 2008. It is located in an underground tunnel 27km in circumference, and when fully operational, will be the world's largest and highest energy particle accelerator. It is hoped that it will provide evidence for the existence of the Higgs boson, the last remaining particle of the socalled Standard Model of particle physics. The quantity of data that will be generated by the LHC is roughly equivalent to that of the European telecommunications network, but this will be boiled down to just a few numbers. After a brief introduction, this talk will outline elements of the statistical problem of detecting the presence of a particle, and then sketch how higher order likelihood asymptotics may be used for signal detection in this context. The work is joint with Nicola Sartori, of the Università Ca' Foscari, in Venice. 

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 Dbrane charges take values
in the Ktheory of spacetime, rather than in integral cohomology as
one might have expected. I will also explore the mathematical
consequences of a particular symmetry, called Tduality, in this context.
I will give an intuitive introduction into Dbranes and Ktheory.
No prior knowledge about either String Theory, Dbranes or Ktheory
is required. 

Puzzlebased learning: Introduction to mathematics 15:10 Fri 23 May, 2008 :: LG29 Napier Building University of Adelaide :: Prof. Zbigniew Michalewicz :: School of Computer Science, University of Adelaide
Media...The talk addresses a gap in the educational curriculum for 1st year students by proposing a new course that aims at getting students to think about how to frame and solve unstructured problems. The idea is to increase the student's mathematical awareness and problemsolving skills by discussing a variety of puzzles. The talk makes an argument that this approach  called PuzzleBased Learning  is very beneficial for introducing mathematics, critical thinking, and problemsolving skills.
The new course has been approved by the University of Adelaide for Faculty of Engineering, Computer Science, and Mathematics. Many other universities are in the process of introducing such a course. The course will be offered in two versions: (a) fullsemester course and (b) a unit within general course (e.g. Introduction to Engineering). All teaching materials (power point slides, assignments, etc.) are being prepared. The new textbook (PuzzleBased Learning: Introduction to Critical Thinking, Mathematics, and Problem Solving) will be available from June 2008. The talk provides additional information on this development.
For further information see http://www.PuzzleBasedlearning.edu.au/ 

What on Earth is Computational Advertising? 15:10 Wed 28 Jan, 2009 :: Napier G03 :: Dr John Tomlin :: Yahoo! Research Labs
This talk will begin with a brief introduction to, and
overview of, the topic we have come to call "computational advertising",
by which we mean the algorithmic techniques useful for the optimal
placement, scheduling and context of online advertisements. Such
advertisements encompass a large and growing fraction of the advertising
industry, and, in the forms of display advertising, content match, and
search marketing, bring in a large fraction of the income derived from
the web. In addition to the overview, we give two examples of
optimization models applied to problems in sponsored search and display
advertising. 

Boltzmann's Equations for Suspension Flow in Porous Media and Correction of the Classical Model 15:10 Fri 13 Mar, 2009 :: Napier LG29 :: Prof Pavel Bedrikovetsky :: University of Adelaide
Suspension/colloid transport in porous media is a basic phenomenon in environmental, petroleum and chemical engineering. Suspension of particles moves through porous media and particles are captured by straining or attraction. We revise the classical equations for particle mass balance and particle capture kinetics and show its nonrealistic behaviour in cases of large dispersion and of flowfree filtration. In order to resolve the paradoxes, the porescale model is derived. The model can be transformed to Boltzmann equation with particle distribution over pores. Introduction of sinksource terms into Boltzmann equation results in much more simple calculations if compared with the traditional ChapmanEnskog averaging procedure. Technique of projecting operators in Hilbert space of Fourier images is used. The projection subspace is constructed in a way to avoid dependency of averaged equations on sinksource terms. The averaging results in explicit expressions for particle flux and capture rate. The particle flux expression describes the effect of advective particle velocity decrease if compared with the carrier water velocity due to preferential capture of "slow" particles in small pores. The capture rate kinetics describes capture from either advective or diffusive fluxes. The equations derived exhibit positive advection velocity for any dispersion and particle capture in immobile fluid that resolves the abovementioned paradox.
Finally, we discuss validation of the model for propagation of contaminants in aquifers, for filtration, for potable water production by artesian wells, for formation damage in oilfields. 

Sloshing in tanks of liquefied natural gas (LNG) vessels 15:10 Wed 22 Apr, 2009 :: Napier LG29 :: Prof. Frederic Dias :: ENS, Cachan
The last scientific conversation I had with Ernie Tuck was on liquid impact. As a matter of fact, we discussed the paper by J.H. Milgram, Journal of Fluid Mechanics 37 (1969), entitled "The motion of a fluid in a cylindrical container with a free surface following vertical impact."
Liquid impact is a key issue in sloshing and in particular in sloshing in tanks of LNG vessels. Numerical simulations of sloshing have been performed by various groups, using various types of numerical methods. In terms of the numerical results, the outcome is often impressive, but the question remains of how relevant these results are when it comes to determining impact pressures. The numerical models are too simplified to reproduce the high variability of the measured pressures. In fact, for the time being, it is not possible to simulate accurately both global and local effects. Unfortunately it appears that local effects predominate over global effects when the behaviour of pressures is considered.
Having said this, it is important to point out that numerical studies can be quite useful to perform sensitivity analyses in idealized conditions such as a liquid mass falling under gravity on top of a horizontal wall and then spreading along the lateral sides. Simple analytical models inspired by numerical results on idealized problems can also be useful to predict trends.
The talk is organized as follows: After a brief introduction on the sloshing problem and on scaling laws, it will be explained to what extent numerical studies can be used to improve our understanding of impact pressures. Results on a liquid mass hitting a wall obtained by a finitevolume code with interface reconstruction as well as results obtained by a simple analytical model will be shown to reproduce the trends of experiments on sloshing.
This is joint work with L. Brosset (GazTransport & Technigaz), J.M. Ghidaglia (ENS Cachan) and J.P. Braeunig (INRIA). 

Buildings 15:10 Fri 9 Oct, 2009 :: MacBeth Lecture Theatre :: Prof Guyan Robertson :: University of Newcastle, UK
Buildings were created by J. Tits in order to give a systematic geometric interpretation of simple Lie groups (and of simple algebraic groups). Buildings have since found applications in many areas of mathematics. This talk will give an informal introduction to these beautiful objects. 

Integrable systems: noncommutative versus commutative 14:10 Thu 4 Mar, 2010 :: School Board Room :: Dr Cornelia Schiebold :: Mid Sweden University
After a general introduction to integrable systems, we will explain an
approach to their solution theory, which is based on Banach space theory. The
main point is first to shift attention to noncommutative integrable systems and
then to extract information about the original setting via projection techniques.
The resulting solution formulas turn out to be particularly wellsuited to the
qualitative study of certain solution classes. We will show how one can obtain
a complete asymptotic description of the so called multiple pole solutions, a
problem that was only treated for special cases before. 

Introduction to mirror symmetry and the Fukaya category I 13:10 Thu 15 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Introduction to mirror symmetry and the Fukaya category II 13:10 Fri 16 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Adjoint methods for adaptive error control, optimization, and uncertainty quantification 15:10 Fri 16 Jul, 2010 :: Napier G03 :: Dr Varis Carey :: Colorado State University
We give an introduction to the use of adjoint equations (and solutions) for numerical error control and
solution enhancement of PDEs. In addition, the same equations can be used for optimization routines and
uncertainty quantification. We discuss the modification of these methods in the context of
operator splitting and to nonvariational (e.g. finite volume) methods. Finally, we conclude with an application
of the method to the shallow water equations and discuss some of the hurdles that need to be overcome
when extending adjoint methodologies to ocean and atmospheric modeling. 

Introduction to mirror symmetry and the Fukaya category III 13:10 Mon 19 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Introduction to mirror symmetry and the Fukaya category IV 13:10 Tue 20 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


Introduction to mirror symmetry and the Fukaya category V 13:10 Wed 21 Jul, 2010 :: Napier G04 :: Dr Mohammed Abouzaid, IGA Lecturer :: Clay Research Fellow, MIT
I shall give an overview of recent progress in homological mirror symmetry, both in clarifying our conceptual understanding of how the sign of the canonical bundle affects the behaviour of the mirror, and in obtaining concrete examples where the mirror conjecture has now been verified. (This is a twohour talk.)


EynardOrantin invariants and enumerative geometry 13:10 Fri 6 Aug, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Dr Paul Norbury :: University of Melbourne
As a tool for studying enumerative problems in geometry Eynard and Orantin associate multilinear differentials to any plane curve. Their work comes from matrix models but does not require matrix models (for understanding or calculations). In some sense they describe deformations of complex structures of a curve and conjectural relationships to deformations of Kahler structures of an associated object. I will give an introduction to their invariants via explicit examples, mainly to do with the moduli space of Riemann surfaces, in which the plane curve has genus zero. 

Contraction subgroups in locally compact groups 13:10 Fri 17 Sep, 2010 :: Ingkarni Wardli B20 (Suite 4) :: Prof George Willis :: University of Newcastle
For each automorphism, $\alpha$, of the locally compact group $G$ there is a corresponding {\sl contraction subgroup\/}, $\hbox{con}(\alpha)$, which is the set of $x\in G$ such that $\alpha^n(x)$ converges to the identity as $n\to \infty$. Contractions subgroups are important in representation theory, through the Mautner phenomenon, and in the study of convolution semigroups.
If $G$ is a Lie group, then $\hbox{con}(\alpha)$ is automatically closed, can be described in terms of eigenvalues of $\hbox{ad}(\alpha)$, and is nilpotent. Since any connected group may be approximated by Lie groups, contraction subgroups of connected groups are thus well understood. Following a general introduction, the talk will focus on contraction subgroups of totally disconnected groups. A criterion for nontriviality of $\hbox{con}(\alpha)$ will be described (joint work with U.~Baumgartner) and a structure theorem for $\hbox{con}(\alpha)$ when it is closed will be presented (joint with H.~Gl\"oeckner). 

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. 

Bioinspired computation in combinatorial optimization: algorithms and their computational complexity 15:10 Fri 11 Mar, 2011 :: 7.15 Ingkarni Wardli :: Dr Frank Neumann :: The University of Adelaide
Media...Bioinspired computation methods, such as evolutionary algorithms and ant colony
optimization, are being applied successfully to complex engineering and
combinatorial optimization problems. The computational complexity analysis of
this type of algorithms has significantly increased the theoretical
understanding of these successful algorithms. In this talk, I will give an
introduction into this field of research and present some important results
that we achieved for problems from combinatorial optimization. These results
can also be found in my recent textbook "Bioinspired Computation in
Combinatorial Optimization  Algorithms and Their Computational Complexity". 

Statistical challenges in molecular phylogenetics 15:10 Fri 20 May, 2011 :: Mawson Lab G19 lecture theatre :: Dr Barbara Holland :: University of Tasmania
Media...This talk will give an introduction to the ways that mathematics and statistics gets used in the inference of evolutionary (phylogenetic) trees. Taking a modelbased approach to estimating the relationships between species has proven to be an enormously effective, however, there are some tricky statistical challenges that remain. The increasingly plentiful amount of DNA sequence data is a boon, but it is also throwing a spotlight on some of the shortcomings of current best practice particularly in how we (1) assess the reliability of our phylogenetic estimates, and (2) how we choose appropriate models. This talk will aim to give a general introduction this area of research and will also highlight some results from two of my recent PhD students. 

Introduction to functional data analysis with applications to proteomics data 11:10 Thu 30 Jun, 2011 :: 7.15 Ingkarni Wardli :: A/Prof Inge Koch :: School of Mathematical Sciences


The Selberg integral 15:10 Fri 5 Aug, 2011 :: 7.15 Ingkarni Wardli :: Prof Ole Warnaar :: University of Queensland
Media...In this talk I will give a gentle introduction to the mathematics surrounding the Selberg integral. Selberg's integral, which first appeared in two rather unusual papers by Atle Selberg in the 1940s, has become famous as much for its association with (other) mathematical greats such as Enrico Bombieri and Freeman Dyson as for its importance in algebra (Coxeter groups), geometry (hyperplane arrangements) and number theory (the Riemann hypothesis). In this talk I will review the remarkable history of the Selberg integral and discuss some of its early applications. Time permitting I will end the talk by describing some of my own, ongoing work on Selberg integrals related to Lie algebras. 

IGAAMSI Workshop: Groupvalued moment maps with applications to mathematics and physics 10:00 Mon 5 Sep, 2011 :: 7.15 Ingkarni Wardli
Media...Lecture series by Eckhard Meinrenken, University of Toronto.
Titles of individual lectures: 1) Introduction to Gvalued moment maps. 2) Dirac geometry and Witten's volume formulas.
3) DixmierDouady theory and prequantization. 4) Quantization of groupvalued moment maps. 5) Application to Verlinde formulas. These lectures will be supplemented by additional talks by invited speakers. For more details, please see the conference webpage. 

Twisted Morava Ktheory 13:10 Fri 9 Sep, 2011 :: 7.15 Ingkarni Wardli :: Dr Craig Westerland :: University of Melbourne
Morava's extraordinary Ktheories K(n) are a family of generalized cohomology theories which behave in some ways like Ktheory (indeed, K(1) is mod 2 Ktheory). Their construction exploits Quillen's description of cobordism in terms of formal group laws and LubinTate's methods in class field theory for constructing abelian extensions of number fields. Constructed from homotopytheoretic methods, they do not admit a geometric description (like deRham cohomology, Ktheory, 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 Ktheory in this setting. Traditionally, Ktheory is twisted by a threedimensional cohomology class; in this case, K(n) admits twists by (n+2)dimensional classes. This work is joint with Hisham Sati. 

What is a selfsimilar group? 15:10 Fri 20 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Murray Elder :: University of Newcastle
Media...I will give a brief introduction to the theory of
selfsimilar groups, focusing on a couple of pertinent examples:
Grigorchuk's group of intermediate growth, and the basilica group.


A brief introduction to Support Vector Machines 12:30 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Tyman Stanford :: University of Adelaide
Media...Support Vector Machines (SVMs) are used in a variety of contexts for a range of purposes including regression, feature selection and classification. To convey the basic principles of SVMs, this presentation will focus on the application of SVMs to classification. Classification (or discrimination), in a statistical sense, is supervised model creation for the purpose of assigning future observations to a group or class. An example might be determining healthy or diseased labels to patients from p characteristics obtained from a blood sample.
While SVMs are widely used, they are most successful when the data have one or more of the following properties:
The data are not consistent with a standard probability distribution.
The number of observations, n, used to create the model is less than the number of predictive features, p. (The socalled smalln, bigp problem.)
The decision boundary between the classes is likely to be nonlinear in the feature space.
I will present a short overview of how SVMs are constructed, keeping in mind their purpose. As this presentation is part of a double postgrad seminar, I will keep it to a maximum of 15 minutes.


Introduction to quantales via axiomatic analysis 13:10 Fri 15 Jun, 2012 :: Napier LG28 :: Dr Ittay Weiss :: University of the South Pacific
Quantales were introduced by Mulvey in 1986 in the context of noncommutative topology with the aim of providing a concrete noncommutative framework for the foundations of quantum mechanics. Since then quantales found applications in other areas as well, among others in the work of Flagg. Flagg considers certain special quantales, called value quantales, that are desigend to capture the essential properties of ([0,\infty],\le,+) that are relevant for analysis. The result is a well behaved theory of value quantale enriched metric spaces. I will introduce the notion of quantales as if they were desigend for just this purpose, review most of the known results (since there are not too many), and address a some new results, conjectures, and questions. 

2012 AMSISSAI Lecture: Approximate Bayesian computation (ABC): advances and limitations 11:00 Fri 13 Jul, 2012 :: Engineering South S112 :: Prof Christian Robert :: Universite ParisDauphine
Media...The lack of closed form likelihoods has been the bane of Bayesian computation for many years and, prior to the introduction of MCMC methods, a strong impediment to the propagation of the Bayesian paradigm. We are now facing models where an MCMC completion of the model towards closedform likelihoods seems unachievable and where a further degree of approximation appears unavoidable. In this talk, I will present the motivation for approximative Bayesian computation (ABC) methods, the consistency results already available, the various Monte Carlo implementations found in the current literature, as well as the inferential, rather than computational, challenges set by these methods. A recent advance based on empirical likelihood will also be discussed. 

Geometric quantisation in the noncompact setting 13:10 Fri 14 Sep, 2012 :: Engineering North 218 :: Dr Peter Hochs :: Leibniz University, Hannover
Traditionally, the geometric quantisation of an action by a compact Lie group on a compact symplectic manifold is defined as the equivariant index of a certain Dirac operator. This index is a welldefined formal difference of finitedimensional representations, since the Dirac operator is elliptic and the manifold and the group in question are compact. From a mathematical and physical point of view however, it is very desirable to extend geometric quantisation to noncompact groups and manifolds. Defining a suitable index is much harder in the noncompact setting, but several interesting results in this direction have been obtained. I will review the difficulties connected to noncompact geometric quantisation, and some of the solutions that have been proposed so far, mainly in connection to the "quantisation commutes with reduction" principle. (An introduction to this principle will be given in my talk at the Colloquium on the same day.)


Quantisation commutes with reduction 15:10 Fri 14 Sep, 2012 :: B.20 Ingkarni Wardli :: Dr Peter Hochs :: Leibniz University Hannover
Media...The "Quantisation commutes with reduction" principle is an idea from physics, which has powerful applications in mathematics. It basically states that the ways in which symmetry can be used to simplify a physical system in classical and quantum mechanics, are compatible. This provides a strong link between the areas in mathematics used to describe symmetry in classical and quantum mechanics: symplectic geometry and representation theory, respectively. It has been proved in the 1990s that quantisation indeed commutes with reduction, under the important assumption that all spaces and symmetry groups involved are compact. This talk is an introduction to this principle and, if time permits, its mathematical relevance. 

Introduction to pairings in cryptography 13:10 Fri 21 Sep, 2012 :: Napier 209 :: Dr Naomi Benger :: University of Adelaide
From cryptanalysis to a powerful tool which made identity based cryptography possible, pairings have a range of applications in cryptography. I will present basic background (algebraic geometry) needed to understand pairings, hard problems associated with pairings and protocols which use pairings. 

Moduli spaces of instantons in algebraic geometry and physics 15:10 Fri 19 Oct, 2012 :: B.20 Ingkarni Wardli :: Prof Ugo Bruzzo :: International School for Advanced Studies Trieste
Media...I will give a quick introduction to the notion of instanton, stressing its role in physics and in mathematics.
I will also show how algebraic geometry provides powerful tools to study the geometry of the moduli spaces of instantons. 

Hyperplane arrangements and tropicalization of linear spaces 10:10 Mon 17 Dec, 2012 :: Ingkarni Wardli B17 :: Dr Graham Denham :: University of Western Ontario
I will give an introduction to a sequence of ideas in tropical
geometry, the tropicalization of linear spaces. In the beginning, a construction due to De Concini and Procesi (wonderful models, 1995) gave a combinatorially explicit description of various iterated blowups of projective spaces along (proper transforms of) linear subspaces. A decade later, Tevelev's notion of tropical compactifications led to, in particular, a new view of the wonderful models and their intersection theory in terms of the theory of toric varieties (via work of FeichtnerSturmfels, FeichtnerYuzvinsky, ArdilaKlivans, and others). Recently, these ideas have played a role in Huh and Katz's proof of a longstanding conjecture in combinatorics. 

A multiscale approach to reactiondiffusion processes in domains with microstructure 15:10 Fri 15 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Malte Peter :: University of Augsburg
Media...Reactiondiffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multiscale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation.
The talk will give an introduction to multiscale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, a few aspects of solving the resulting systems of equations numerically will also be discussed. 

Diffeological spaces and differentiable stacks 12:10 Fri 10 May, 2013 :: Ingkarni Wardli B19 :: Dr David Roberts :: University of Adelaide
The category of finitedimensional smooth manifolds gives rise to interesting structures outside of itself, two examples being mapping spaces and classifying spaces. Diffeological spaces are a notion of generalised smooth space which form a cartesian closed category, so all fibre products and all mapping spaces of smooth manifolds exist as diffeological spaces. Differentiable stacks are a further generalisation that can also deal with moduli spaces (including classifying spaces) for objects with automorphisms. This talk will give an introduction to this circle of ideas. 

Invariant Theory: The 19th Century and Beyond 15:10 Fri 21 Jun, 2013 :: B.18 Ingkarni Wardli :: Dr Jarod Alper :: Australian National University
Media...A central theme in 19th century mathematics was invariant theory, which was viewed as a bridge between geometry and algebra. David Hilbert revolutionized the field with two seminal papers in 1890 and 1893 with techniques such as Hilbert's basis theorem, Hilbert's Nullstellensatz and Hilbert's syzygy theorem that spawned the modern field of commutative algebra. After Hilbert's groundbreaking work, the field of invariant theory remained largely inactive until the 1960's when David Mumford revitalized the field by reinterpreting Hilbert's ideas in the context of algebraic geometry which ultimately led to the influential construction of the moduli space of smooth curves. Today invariant theory remains a vital research area with connections to various mathematical disciplines: representation theory, algebraic geometry, commutative algebra, combinatorics and nonlinear differential operators.
The goal of this talk is to provide an introduction to invariant theory with an emphasis on Hilbert's and Mumford's contributions. Time permitting, I will explain recent research with Maksym Fedorchuk and David Smyth which exploits the ideas of Hilbert, Mumford as well as Kempf to answer a classical question concerning the stability of algebraic curves. 

Lost in Space: Point Pattern Matching and Astrometry 12:35 Mon 14 Oct, 2013 :: B.19 Ingkarni Wardli :: Annie Conway :: University of Adelaide
Astrometry is the field of research that concerns the positions of objects in space. This can be useful for satellite tracking where we would like to know accurate positions of satellites at given times. Telescopes give us some idea of the position, but unfortunately they are not very precise.
However, if a photograph of a satellite has stars in the background, we can use that information to refine our estimate of the location of the image, since the positions of stars are known to high accuracy and are readily available in star catalogues. But there are billions of stars in the sky so first we would need to determine which ones we're actually looking at.
In this talk I will give a brief introduction to astrometry and walk through a point pattern matching algorithm for identifying stars in a photograph. 

Braids and entropy 10:10 Fri 8 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Burglind Joricke :: Australian National University
This talk will be a brief introduction to some aspects of braid theory and to entropy, to provide background for the speaker's talk at 12:10 pm the same day.


Braids, conformal module and entropy 12:10 Fri 8 Nov, 2013 :: Ingkarni Wardli B19 :: Prof Burglind Joricke :: Australian National University
I will discuss two invariants of conjugacy classes of braids.
The first invariant is the conformal module which implicitly occurred
already in a paper of Gorin and Lin in connection with their
interest in Hilbert's 13th problem. The second is a popular
dynamical invariant, the entropy. It appeared in connection
with Thurston's theory of surface homeomorphisms.
It turns out that these invariants are related: They are inversely
proportional.
In a preparatory talk (at 10:10 am) I will give a brief introduction to some aspects of braid theory and to entropy.


A gentle introduction to bubble evolution in HeleShaw flows 15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT
A HeleShaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a HeleShaw cell that is otherwise filled with viscous fluid, we can observe a bubble of air growing in size. The process is highly unstable, and the bubble boundary expands in an uneven fashion, leading to striking fingering patterns (look up HeleShaw cell or SaffmanTaylor instability on YouTube). From a mathematical perspective, modelling these HeleShaw flows is interesting because the governing equations are sufficiently ``simple'' that a considerable amount of analytical progress is possible. Indeed, there is no other context in which (genuinely) twodimensional moving boundary problems are so tractable. More generally, HeleShaw flows are important as they serve as prototypes for more complicated (and important) physical processes such as crystal growth and diffusion limited aggregation. I will give an introduction to some of the main ideas and summarise some of my present research in this area.


Lefschetz fixed point theorem and beyond 12:10 Fri 2 May, 2014 :: Ingkarni Wardli B20 :: Hang Wang :: University of Adelaide
A Lefschetz number associated to a continuous map on a closed manifold is a topological invariant determined by the geometric information near the neighbourhood of fixed point set of the map. After an introduction of the Lefschetz fixed point theorem, we shall use the Diracdual Dirac method to derive the Lefschetz number on Ktheory level. The method concerns the comparison of the Dirac operator on the manifold and the Dirac operator on some submanifold. This method can be generalised to several interesting situations when the manifold is not necessarily compact. 

Stochastic models of evolution: Trees and beyond 15:10 Fri 16 May, 2014 :: B.18 Ingkarni Wardli :: Dr Barbara Holland :: The University of Tasmania
Media...In the first part of the talk I will give a general introduction to phylogenetics, and discuss some of the mathematical and statistical issues that arise in trying to infer evolutionary trees. In particular, I will discuss how we model the evolution of DNA along a phylogenetic tree using a continuous time Markov process.
In the second part of the talk I will discuss how to express the twostate continuoustime Markov model on phylogenetic trees in such a way that allows its extension to more general models. In this framework we can model convergence of species as well as divergence (speciation). I will discuss the identifiability (or otherwise) of the models that arise in some simple cases. Use of a statistical framework means that we can use established techniques such as the AIC or likelihood ratio tests to decide if datasets show evidence of convergent evolution. 

Approximate dynamic programming: An introduction 12:10 Mon 11 Aug, 2014 :: B.19 Ingkarni Wardli :: Mingmei Teo :: University of Adelaide
Media...In this talk, I'll attempt to give insights into what is dynamic programming and a common method used to solve dynamic programming problems. Then, we'll explore some issues with this method and introduce the idea of approximate dynamic programming. Finally, I'll very briefly describe why I'm interested in approximate dynamic programming. 

Tduality 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 squarezero 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 Tduality in this setting. This is based on joint work in progress with V. Mathai. 

Dynamic programming and optimal scoring rates in cricket 12:10 Mon 30 Mar, 2015 :: Napier LG29 :: Mingmei Teo :: University of Adelaide
Media...With the cricket world cup having reached it's exciting conclusion and many world cup batting records being rewritten at this world cup, we look back to the year 1987 where batting occurred at a more sedate pace and totals of 300+ were a rarity. In this talk, I'll discuss how dynamic programming has been applied to oneday cricket to determine optimal scoring rates and I'll also attempt to give a brief introduction into what is dynamic programming and a common method used to solve dynamic programming problems. 

A relaxed introduction to resamplingbased multiple testing 12:10 Mon 10 Aug, 2015 :: Benham Labs G10 :: Ngoc Vo :: University of Adelaide
Media...Pvalues and false positives are two phrases that you commonly see thrown around in scientific literature. More often than not, experimenters and analysts are required to quote pvalues as a measure of statistical significance â how strongly does your evidence support your hypothesis? But what happens when this "strong evidence" is just a coincidence? What happens if you have lots of theses hypotheses â up to tens of thousands â to test all at the same time and most of your significant findings end up being just "coincidences"? 

Harmonic analysis of HodgeDirac operators 12:10 Fri 13 May, 2016 :: Eng & Maths EM205 :: Pierre Portal :: Australian National University
Media...When the metric on a Riemannian manifold is perturbed in a rough (merely bounded and measurable) manner, do basic estimates involving the Hodge Dirac operator $D = d+d^*$ remain valid? Even in the model case of a perturbation of the euclidean metric on $\mathbb{R}^n$, this is a difficult question. For instance, the fact that the $L^2$ estimate $\Du\_2 \sim \\sqrt{D^{2}}u\_2$ remains valid for perturbed versions of $D$ was a famous conjecture made by Kato in 1961 and solved, positively, in a ground breaking paper of Auscher, Hofmann, Lacey, McIntosh and Tchamitchian in 2002. In the past fifteen years, a theory has emerged from the solution of this conjecture, making rough perturbation problems much more tractable. In this talk, I will give a general introduction to this theory, and present one of its latest results: a flexible approach to $L^p$ estimates for the holomorphic functional calculus of $D$. This is joint work with D. Frey (Delft) and A. McIntosh (ANU).


Symmetric functions and quantum integrability 15:10 Fri 30 Sep, 2016 :: Napier G03 :: Dr Paul ZinnJustin :: University of Melbourne/Universite Pierre et Marie Curie
Media...We'll discuss an approach to studying families of symmetric polynomials which is based on ''quantum integrability'', that is, on the use of exactly solvable twodimensional lattice models. We'll first explain the general strategy on the simplest case, namely Schur polynomials, with the introduction of a model of lattice paths (a.k.a. fivevertex model). We'll then discuss recent work (in collaboration with M. Wheeler) that extends this approach to HallLittlewood polynomials and Grothendieck polynomials, and some applications of it. 

Introduction to Lorentz Geometry: Riemann vs Lorentz 12:10 Fri 18 Nov, 2016 :: Engineering North N132 :: Abdelghani Zeghib :: Ecole Normale Superieure de Lyon
Media...The goal is to compare Riemannian and Lorentzian geometries and see what one loses and wins when going from the Riemann to Lorentz. Essentially, one loses compactness and ellipticity, but wins causality structure and mathematical and physical situations
when natural Lorentzian metrics emerge.


Complexity of 3Manifolds 15:10 Fri 23 Mar, 2018 :: Horace Lamb 1022 :: A/Prof Stephan Tillmann :: University of Sydney
In this talk, I will give a general introduction to complexity of
3manifolds and explain the connections between combinatorics, algebra,
geometry, and topology that arise in its study.
The complexity of a 3manifold is the minimum number of tetrahedra in a
triangulation of the manifold. It was defined and first studied by Matveev
in 1990. The complexity is generally difficult to compute, and various
upper and lower bounds have been derived during the last decades using
fundamental group, homology or hyperbolic volume.
Effective bounds have only been found in joint work with Jaco, Rubinstein
and, more recently, Spreer. Our bounds not only allowed us to determine the
first infinite classes of minimal triangulations of closed 3manifolds, but
they also lead to a structure theory of minimal triangulations of
3manifolds. 

Knot homologies 15:10 Fri 4 May, 2018 :: Horace Lamb 1022 :: Dr Anthony Licata :: Australian National University
The last twenty years have seen a lot of interaction between lowdimensional topology and representation theory. One facet of this interaction concerns "knot homologies," which are homological invariants of knots; the most famous of these, Khovanov homology, comes from the higher representation theory of sl_2. The goal of this talk will be to give a gentle introduction to this subject to nonexperts by telling you a bit about Khovanov homology. 

Interactive theorem proving for mathematicians 15:10 Fri 5 Oct, 2018 :: Napier 208 :: A/Prof Scott Morrison :: Australian National University
Mathematicians use computers to write their proofs (LaTeX), and to do their calculations (Sage, Mathematica, Maple, Matlab, etc, as well as custom code for simulations or searches). However today we rarely use computers to help us to construct and understand proofs.
There is a long tradition in computer science of interactive and automatic theorem proving; particularly today these are important tools in engineering correct software, as well as in optimisation and compilation. There have been some notable examples of formalisation of modern mathematics (e.g. the odd order theorem, the Kepler conjecture, and the fourcolour theorem). Even in these cases, huge engineering efforts were required to translate the mathematics to a form a computer could understand. Moreover, in most areas of research there is a huge gap between the interests of human mathematicians and the abilities of computer provers.
Nevertheless, I think it's time for mathematicians to start getting interested in interactive theorem provers! It's now possible to write proofs, and write tools that help write proofs, in languages which are expressive enough to encompass most of modern mathematics, and ergonomic enough to use for general purpose programming.
I'll give an informal introduction to dependent type theory (the logical foundation of many modern theorem provers), some examples of doing mathematics in such a system, and my experiences working with mathematics students in these systems. 

An Introduction to Ricci Flow 11:10 Fri 19 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg
In these three talks we give an introduction to Ricci flow and present some applications thereof.
After introducing the Ricci flow we present some theorems and arguments from the theory of linear and nonlinear parabolic equations. We explain why this theory guarantees that there is always a solution to the Ricci flow for a short time for any given smooth initial metric on a compact manifold without boundary.
We calculate evolution equations for certain geometric quantities, and present some examples of maximum principle type arguments. In the last lecture we present some geometric results which are derived with the help of the Ricci flow. 
News matching "Introduction to pairings in cryptography" 
IGAAMSI Workshop: Groupvalued moment maps with applications to mathematics and physics (5–9 September 2011) Lecture series by Eckhard Meinrenken, University of Toronto. Titles of
individual lectures: 1) Introduction to Gvalued moment maps. 2) Dirac
geometry and Witten's volume formulas. 3) DixmierDouady theory and
prequantization. 4) Quantization of groupvalued moment maps. 5)
Application to Verlinde formulas. These lectures will be supplemented by
additional talks by invited speakers. For more details, please see the
conference webpage
Posted Wed 27 Jul 11.More information... 
Publications matching "Introduction to pairings in cryptography"Publications 

Invariant differential pairings Kroeske, Jens, Universitas Comeniana. Acta Mathematica 77 (215–244) 2008  A sequence approach to linear perfect hash families Barwick, Susan; Jackson, WenAi, Designs Codes and Cryptography 45 (95–121) 2007  Projective aspects of the AES inversion Jackson, WenAi; Murphy, S, Designs Codes and Cryptography 43 (167–179) 2007  Symmetries and invariant differential pairings Eastwood, Michael, Symmetry, Integrability and Geometry: Methods and Applications 113 (1–10) 2007  The polynomial degree of the Grassmannian G(1, n, q) of lines in finite projective space PG(n, q) Glynn, David; Maks, J; Casse, Rey, Designs Codes and Cryptography 40 (335–341) 2006  A general approach to robust web metering Barwick, Susan; Jackson, WenAi; Martin, K, Designs Codes and Cryptography 36 (5–27) 2005  An optimal multisecret threshold scheme construction Barwick, Susan; Jackson, WenAi, Designs Codes and Cryptography 37 (367–389) 2005  An introduction to programming and numerical methods in MATLAB Otto, S; Denier, James, (SpringerVerlag) 2005  The interpretation of uncontrolled beforeandafter studies: As demonstrated by recent studies of the introduction of medical emergency teams Moran, John; Solomon, Patricia, Critical care and Resuscitation 7 (153–159) 2005  Spreads of T2(O), aflocks and Ovals Brown, Matthew; O'Keefe, Christine; Payne, S; Penttila, T; Royle, G, Designs Codes and Cryptography 31 (251–282) 2004  Measure Theory and Filtering: Introduction and Applications Aggoun, L; Elliott, Robert, (Cambridge University Press) 2004  Introduction to ChernSimons gauge theory on general 3manifolds Adams, David, chapter in Mathematical methods in physics (World Scientific Publishing) 1–43, 2000 
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