
CARMASponsored Seminar Series: Colloquia, Seminars and More.

[Note: events are listed by descending date.]
 CARMA COLLOQUIUM
 Speaker: Prof. Joseph Rosenblatt, Department of Mathematical Sciences, Indiana UniversityPurdue University Indianapolis
 Title: Quantization using random, Diophantine, and dynamical processes
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 17^{th} May 2018
 Abstract:
The use of various methods to obtain close to optimal quantization leads to interesting questions about the behavior of random processes, Diophantine approximation, ergodic maps, shrinking targets, and other related constructions. The goal in all of these approaches to quantization is the speed of decrease of the error, coupled with the simplicity and concreteness of the process employed.
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 CARMA COLLOQUIUM
 Speaker: Prof. Florian Breuer, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: The Parallel Worlds of Number Theory
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} May 2018
 Abstract:
There is an intriguing analogy between number fields and function fields. If we view classical Number Theory as the study of the ring of integers and its extensions, then function field arithmetic is the study of the ring of polynomials over a finite field and its extensions. According to this analogy, most constructions and phenomena in classical Number Theory, ranging from the elementary theorems of Euler, Fermat and Wilson, to the Riemann Hypothesis, Elliptic curves, class field theory and modular forms all have their function field analogues. I will give a panoramic tour of some of these constructions and highlight their similarities and differences to their classical counterparts.
This lecture should be accessible to advanced undergraduate students.
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 CARMA COLLOQUIUM
 Speaker: Prof Brigitte ForsterHeinlein, University of Passau
 Title: The commutative diagram of signal processing
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 31^{st} Oct 2017
 Abstract:
We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the PaleyWiener Theorem. We start from a generalization of the PaleyWiener theorem and consider entire functions with specific growth properties along halflines. Our main result shows that the growth exponents are directly related to the shape of the corresponding indicator diagram, e.g., its side lengths. Since many results from sampling theory are derived with the help from a more general function theoretic point of view (the most prominent example for this is the PaleyWiener Theorem itself), we motivate that a closer examination and understanding of the Bernstein spaces and the corresponding commutative diagrams can—via a limiting process to the straight line interval [−A,A]—yield new insights into the Lp(R)sampling theory. This is joint work with Gunter Semmler, Technische Universität Bergakademie Freiberg, Germany.
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 CARMA COLLOQUIUM
 Speaker: Peter Massopust, Technical University of Munich
 Title: BSplines and Beyond
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 12^{th} Oct 2017
 Abstract:
Schoenberg’s polynomial cardinal Bsplines of order $n$ provide a family of compactly supported $C^{n2}$functions. We present several generalizations of these Bsplines, discuss their properties, and relate them to fractional difference and differentiation operators. Potential applications are mentioned.
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 CARMA COLLOQUIUM
 Speaker: Dr Michael Assis, CARMA, The University of Newcastle
 Title: Systematic analysis of OEIS generating functions
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 10^{th} Oct 2017
 Abstract:
Given a sequence of integers, one would like to understand the pattern which generates the sequence, as well as its asymptotics. If the sequence is viewed as the coefficients of the series expansion of a function, called its generating function, many questions regarding the sequence can be answered more easily. If the generating function satisfies a linear ODE or a nonlinear algebraic DE, the differential equation can be found if enough terms in the sequence are given. In this talk I'll discuss my implementation in C of such a search, applications, and a systematic search of the entire Online Encyclopedia of Integer Sequences (OEIS) for generating functions.
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 CARMA COLLOQUIUM
 Speaker: Dr Michael Assis, CARMA, The University of Newcastle
 Title: Exactly solved origami statistical mechanics
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Wed, 2^{nd} Aug 2017
 Abstract:
I will discuss how to relate regular origami tilings to vertex models in statistical mechanics. The Miuraori origami pattern has found many uses in engineering as an auxetic metamaterial. I analyze the effect of crease assignment defects on the longrange order properties of the
Miuraori and 4 other foldable lattices. These defects are known to affect the material's compressibility properties, so my exact results help to understand how easy it is to tune an origami metamaterial to have desired compressibility properties by introducing a set density of defects. I have found that certain origami patterns are more easily tunable than others, and conversely, the longrange ordering of some are more stable with respect to defect formation. I have also found analytical expressions for the locations of phase transition points with respect to crease assignment ordering as well as layer ordering.
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 CARMA COLLOQUIUM
 Speaker: Finnur Larusson, The University of Adelaide
 Title: The rough shape of spaces of soap films
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 20^{th} Jun 2017
 Abstract:
The theory of minimal surfaces (a.k.a. soap films) goes back to Euler’s discovery in 1741 that the catenoid is areaminimising. It is still a remarkably vibrant area of research. I will describe recent joint work with Franc Forstneric of the University of Ljubljana, Slovenia. We assemble all minimal surfaces with a given shape into a space. It is an infinitedimensional space. What does it look like? We have been able to determine its "rough shape". I will explain what we mean by "rough shape" and describe the ingredients from complex analysis, differential topology, and homotopy theory that go into our result.
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 CARMA COLLOQUIUM
 Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
 Title: Groups, machines, algae and trees
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 4^{th} Apr 2017
 Abstract:
In a way, mathematics can be seen as a language game, where we use symbols, together with some rewriting rules, to represent objects we are interested in and then ask what can be said about the sequences of symbols (languages) that capture certain phenomena. For example, given a group G with generators a and b, can we recognise (using a computer) the sequences of generators that correspond to nontrivial elements of G? If yes, how strong computer do we need, i.e. how complicated is the language we are studying?
There is a natural duality between various types of computational models and classes of languages that can be recognised by them. Until recently most problems/languages in group theory were classified within the Chomsky hierarchy, but there are more computational models to consider. In the talk I will briefly introduce Lsystems, a family of classes of languages originally developed to model growth of algae, and show that the coword problem in Grigorchuk's group, a group of particularly nice transformations of infinite binary tree, can be seen as a language corresponding to a fairly simple Lsystem.
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 CARMA COLLOQUIUM
 Speaker: Dr Colin Reid, CARMA, The University of Newcastle
 Title: Totally disconnected, locally compact groups
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 28^{th} Mar 2017
 Abstract:
Totally disconnected, locally compact (t.d.l.c.) groups are a large class of topological groups that arise from a few different sources, for instance as automorphism groups of a range of algebraic and combinatorial structures, or from the study of isomorphisms between finite index subgroups of a given group. A general theory has begun to emerge in recent years, based on the interaction between smallscale and largescale structure in t.d.l.c. groups. I will give a survey of some ways in which these groups arise and some of the tools that have been developed for understanding them.
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 CARMA COLLOQUIUM
 Speaker: Saman Eskandarzadeh, unknown or leave blank,
 Title: Conditional value at risk measure applications
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 9^{th} Mar 2017
 Abstract:
In this talk, I will describe the conditional value at risk (CVaR) measure used in modelling risk aversion in decision making problems.
CVaR is a highly consistent risk measure for modelling risk aversion.
I will then present two applications of CVaR. The first application considers all problems that are representable by decision trees. In this application, I show that these problems under the CVaR criterion can be solved efficiently by solving a linear program. In the second application, I consider a basic problem in the area of production planning with random yield. For this problem, I present a risk aversion model. The model is nonconvex. I present an efficient locally optimal solution method and then provide a sufficient optimality condition.
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 CARMA COLLOQUIUM
 Speaker: Dr Dave Robertson, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Semigroup C*algebras
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 7^{th} Mar 2017
 Abstract:
There is to date no overarching classification theorem for C*algebras, which means the theory of C*algebras is an exampledriven field of mathematics. Perhaps the most important class of examples are group C*algebras, which are as old as the field itself. An analogous construction of C*algebras associated to semigroups has been an active area of research among operator algebraists since Coburn’s Theorem regarding the universality of the C*algebra generated a single isometry appeared in the 1960s. In July this year, Newcastle will host the AMSI/AustMS sponsored event "Interactions between operator algebras and semigroups". In this talk I will give a gentle introduction to the theory of semigroup C*algebras and perhaps it will convince some of you to come along and take part in the meeting.
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 CARMA COLLOQUIUM
 Speaker: Michael Bennett, University of British Columbia
 Title: ErdosSelfridge and Supersingularity
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 28^{th} Feb 2017
 Abstract:
In 1975, culminating more than 40 years of published work by Paul Erdos on the problem, he and John Selfridge proved that the product of consecutive integers cannot be a nonzero perfect power. Their proof was a remarkable combination of elementary and graph theoretic arguments. Subsequently, Erdos conjectured that this result can be generalized to a product of consecutive terms in an arithmetic progression, under certain basic assumptions. In this talk, we discuss joint work with Samir Siksek in the direction of proving Erdos' conjecture. Our approach is via techniques based upon the modularity of Galois representations, bounds for the number of supersingular primes for elliptic curves, and analytic estimates for Dirichlet character sums.
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 CARMA COLLOQUIUM
 Speaker: David Broadhurst, School of Physical Sciences, Open University
 Title: Jon Borwein: discoverer, prover, colleague and friend
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Thu, 2^{nd} Feb 2017
 Abstract:
Jonathan Michael Borwein (20 May 1951  2 Aug 2016) had many talents, among which were his abilities to make discoveries in mathematics, to seek tenaciously for proofs of these, and to do both of those things in collegial concert with other workers. In this colloquium I shall give three examples of situation in which I had the pleasure of seeing those talents in action. They concern multiple zeta values, walks on lattices, and modular forms. In each case I shall give a notable identity, comment on its proof, and indicate further work that was provoked by the discovery. The identities in question are chosen to be comprehensible to anyone with an undergraduate education in mathematics and also to people, like myself, who lack that particular qualification.
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 CARMA COLLOQUIUM
 Speaker: A/Prof Chris Kellett, School of Electrical Engineering and Computer Science, The University of Newcastle
 Title: The Social Cost of Carbon  Mitigating Global Warming Whilst Avoiding Economic Collapse
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Wed, 19^{th} Oct 2016
 Abstract:
Many governments and international finance organisations use a carbon price in costbenefit analyses, emissions trading schemes, quantification of energy subsidies, and modelling the impact of climate change on financial assets. The most commonly used value in this context is the social cost of carbon (SCC). Users of the social cost of carbon include the US, UK, German, and other governments, as well as organisations such as the World Bank, the International Monetary Fund, and Citigroup. Consequently, the social cost of carbon is a key factor driving worldwide investment decisions worth many trillions of dollars.
The social cost of carbon is derived using integrated assessment models that combine simplified models of the climate and the economy. One of three dominant models used in the calculation of the social cost of carbon is the Dynamic Integrated model of Climate and the Economy, or DICE. DICE contains approximately 70 parameters as well as several exogenous driving signals such as population growth and a measure of technological progress. Given the quantity of finance tied up in a figure derived from this simple highly parameterized model, understanding uncertainty in the model and capturing its effects on the social cost of carbon is of paramount importance. Indeed, in late January this year the US National Academies of Sciences, Engineering, and Medicine released a report calling for discussion on the various types of uncertainty in the overall SCC estimation approach and addressing how different models used in SCC estimation capture uncertainty.
This talk, which focuses on the DICE model, essentially consists of two parts. In Part One, I will describe the social cost of carbon and the DICE model at a highlevel, and will present some interesting preliminary results relating to uncertainty and the impact of realistic constraints on emissions mitigation efforts. Part one will be accessible to a broad audience and will not require any specific technical background knowledge. In Part Two, I will provide a more detailed description of the DICE model, describe precisely how the social cost of carbon is calculated, and indicate ongoing developments aimed at improving estimates of the social cost of carbon.
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 CARMA COLLOQUIUM
 Speaker: John Mack, The University of Sydney
 Title: The breaking of Japanese Army and Navy codes during WW2
 Location: Room V107, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 12^{th} May 2016
 Abstract:
In 2000, after investigating the published literature(for which I had reason then), I realised that there was clearly confusion surrounding the question of how WW2 Japanese army and navy codes had been broken by the Allies.
Fourteen years later, my academic colleague Peter Donovan and I understood why that was so: the archival documents needed to perform this task, plus the mathematical understanding needed to interpret correctly these documents, had only exposed themselves through our combined researches over this long period. The result, apart from a number of research publications in journals, is our book, "Code Breaking in the Pacific", published by Springer International in 2014.
Both the Imperial Japanese Army (IJA) and the Imperial Japanese Navy (IJN) used an encryption system involving a code book and then a second stage encipherment, a system which we call an additive cipher system, for their major codes – not a machine cipher such as the Enigma machines used widely by German forces in ww2 or the Typex/Sigaba/ECM machines used by the Allies. Thus, the type of attack needed to crack such a system is very different to those described in books about Bletchley Park and its successes against Enigma ciphers.
However, there is a singular difference: while the IJN’s main coding system, known to us as JN25, was broken from its inception and throughout the Pacific War, yielding for example the intelligence information that enabled the battles of the Coral Sea and Midway to occur, or the shooting down of Admiral Yamamoto to be planned, the many IJA coding systems in use were, with one exception, never broken!
I will describe the general structure of additive systems, the rational way developed to attack them and its usual failure in practice, and the "miracle" that enabled JN25 to be broken  probably the bestkept secret of the entire Pacific War: multiples of three! Good maths, but not highly technical!
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 CARMA COLLOQUIUM
 Speaker: Tyrone Ghaswala, University of Waterloo
 Title: Groups, Maps, Covers, and a Touch of Class
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 5^{th} Apr 2016
 Abstract:
Mapping class groups are groups which arise naturally from homeomorphisms of surfaces. They are ubiquitous: from hyperbolic geometry, to combinatorial group theory, to algebraic geometry, to low dimensional topology, to dynamics. Even to this colloquium!
In this talk, I will give a survey of some of the highlights from this beautiful world, focusing on how mapping class groups interact with covering spaces of surfaces. In particular, we will see how a particular order 2 element (the hyperelliptic involution) and its centraliser (the hyperelliptic mapping class group) play an important role, both within the world of mapping class groups and in other areas of mathematics. If time permits, I will briefly touch on some recent joint work with Rebecca Winarski that generalises the hyperelliptic story.
No experience with mapping class groups will be assumed, and this talk will be aimed at a general mathematics audience.
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 CARMA COLLOQUIUM
 Speaker: Prof Tim Pleskac, unknown or leave blank,
 Title: The Dynamic Nature of Confidence
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} Mar 2016
 Abstract:
How confident are you in your choice? Such a simple but important question for people to answer. Yet, capturing how people answer this question has proven challenging for mathematical models of cognition. Part of the challenge has been that these models assume confidence is a static variable based on the same information used to make a decision. In the first part of my talk, I will review my dynamic theory of confidence, twostage dynamic signal detection theory (2DSD). 2DSD is based on the premise that the same evidence accumulation process that underlies choice is used to make confidence judgments, but that postdecisional processing of information contributes to confidence judgments. Thus, 2DSD correctly predicts that the resolution of confidence judgments, or their ability to discriminate between correct and incorrect choices, increases over time. However, I have also found that the dynamics of confidence is driven by other factors including the very act of making a choice. In the second of the part of the talk, I will show how 2DSD and other models derived from classical stochastic theories are unable to parsimoniously account for this stable interference effect of choice. In contrast, quantum random walk modes of evidence accumulation account for this property by treating judgments and decisions as a measurement process by which a definite state is created from an indefinite state. In summary, I hope to show how better understanding the dynamic nature of confidence can provide new methods for improving the accuracy of people’s confidence, but also reveal new properties of the deliberation process including perhaps the quantum nature of evidence accumulation.
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 CARMA COLLOQUIUM
 Speaker: Andrew Rechnitzer, University of British Colombia
 Title: Bounding the entropy of hard squares
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 3^{rd} Mar 2016
 Abstract:
Start labelling the vertices of the square grid with 0's and 1's with the condition that any pair of neighbouring vertices cannot both be labelled 1. If one considers the 1's to be the centres of small squares (rotated 45 degrees) then one has a picture of squareparticles that cannot overlap.
This problem of "hardsquares" appears in different areas of mathematics  for example it has appeared separately as a lattice gas in statistical mechanics, as independent sets in combinatorics and as the goldenmean shift in symbolic dynamics.
A core question in this model is to quantify the number of legal configurations  the entropy. In this talk I will discuss the what is known about the entropy and describe our recent work finding rigorous and precise bounds for hardsquares and related problems.
This is work together with Yaoban Chan.
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 CARMA COLLOQUIUM
 Speaker: Michael Baake, Bielefeld
 Title: Dynamical Systems of numbertheoretic origin in the theory of aperiodic order
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 23^{rd} Feb 2016
 Abstract:
Model sets, which go back to Yves Meyer (1972), are a versatile class of structures with amazing harmonic properties. They are particularly relevant for mathematical quasicrystals. More recently, also systems such as the squarefree integers or the visible lattice points have been studied in this context, leading to the theory of weak model sets. This talk will review some of the development, and introduce some of the concepts in the field.
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 CARMA COLLOQUIUM
 Speaker: Florian Luca, University of the Witwatersrand
 Title: Diophantine mtuples
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 28^{th} Jan 2016
 Abstract:
A diophantine mtuple is a set of mpositive integers {a_1, . . . , a_m} such that the product of any two of them plus 1 is a square. For example, {1, 3, 8, 120} is a Diophantine quadruple found by Fermat. It is known that there are infinitely many such examples with m = 4 and none with m = 6. No example is known with m = 5 but if there exist, then there are only finitely many such.
In my talk, I will survey what is known about this problem, as well as its variations, where one replaces the ring of integers by the ring of integers in some finite extension of Q, or by the field of rational numbers, or one looks at a variant of this problem in the ring of polynomials with coefficients in a field of characteristic zero, or when one replaces the squares by perfect powers of a larger exponent, or by members of some other interesting sequence like the sequence of Fibonacci numbers and so on.
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 CARMA COLLOQUIUM
 Speaker: Dr Faustin Adiceam, University of York
 Title: How far can you see in a forest?
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 22^{nd} Oct 2015
 Abstract:
We will be answering the following question raised by Christopher Bishop:
'Suppose we stand in a forest with tree trunks of radius $r > 0$ and no two trees centered closer than unit distance apart. Can the trees be arranged so that we can never see further than some distance $V < \infty$, no matter where we stand and what direction we look in? What is the size of $V$ in terms of $r$?'
The methods used to study this problem involve Fourier analysis and sharp estimates of exponential sums.
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 CARMA COLLOQUIUM
 Speaker: Karl Dilcher, Mathematics and Statistics, Dalhousie University
 Title: Zeros and irreducibility of gcdpolynomials
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 15^{th} Oct 2015
 Abstract:
We study the family of selfinversive polynomials of degree $n$ whose $j$th
coefficient is $\gcd(n,j)^k$, for a fixed integer $k \geq 1$. We prove
that these polynomials have all of their roots on the unit circle, with
uniform angular distribution. In the process we prove some new results
on Jordan's totient function. We also show that these polynomials
are irreducible, apart from an obvious linear factor, whenever $n$ is a
power of a prime, and conjecture that this holds for all $n$.
Finally we use some of these methods to obtain general results on the zero
distribution of selfinversive polynomials and of their "duals" obtained
from the discrete Fourier transforms of the coefficients sequence.
(Joint work with Sinai Robins).
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 CARMA COLLOQUIUM
 Speaker: Alan Haynes, University of York
 Title: Quasicrystals and Diophantine approximation
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} Sep 2015
 Abstract:
In this talk we will begin with a brief history of the mathematics of aperiodic tilings of Euclidean space, highlighting their relevance to the theory of quasicrystals. Next we will focus on an important collection of point sets, cut and project sets, which come from a dynamical construction and provide us with a mathematical model for quasicrystals. After giving definitions and examples of these sets, we will discuss their relationship with Diophantine approximation, and show how the interplay between these two subjects has recently led to new results in both of them.
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 CARMA COLLOQUIUM
 Speaker: Dr Mojtaba Heydar, ARC Centre for Food and Beverage Supply Chain Optimisation, The University of Newcastle
 Title: Models for cyclic train timetabling and platforming
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 9^{th} Jul 2015
 Abstract:
Managing railway in general and high speed rail in particular is a very complex task which involves many different interrelated decisions in all three strategic, tactical, and operational phases. In this research two different mixed integer linear programing models are presented which are the literature's first models of their kind. In the first model a single line with two different train types is considered. In the second model a cyclic train timetabling and platforming assignment problems are considered and solved to optimality. For this model, methods for obtaining bounds on the first objective function are presented. Some preprocessing techniques to reduce the number of decision variables and constraints are also proposed. Proposed models' objectives are to minimize (1) the cyclic length, called Interval, and (2) the total journey time of all trains dispatched from their origin in each cycle. Here we explicitly consider the minimization of the cycle length using linear constraints and linear objective function. The proposed models are different from and faster than the widelyused Period Event Scheduling Problem (PESP).
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 CARMA COLLOQUIUM
 Speaker: Joe Lakey, New Mexico State University
 Title: Some Mathematical Tools for Analysis of EEG data
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 11^{th} Jun 2015
 Abstract:
Advantages of EEG in studying brain signals include excellent temporal localization
and, potentially, good spatial localization, given good models for source localization in the brain.
Phase synchrony and crossfrequency coupling are two phenomena believed to indicate
cooperation of different brain regions in cognition through messaging via different frequency bands.
To verify these hypotheses requires ability to extract timefrequency localized components
from complex multicomponent EEG data. One such method, empirical mode decompositions,
shows increasing promise through engineering and we will review recent progress on this approach.
Another potential method uses bases or frames of optimally timefrequency localized signals,
socalled prolate spheroidal wave functions. New properties of these functions developed in
joint work with Jeff Hogan will be reviewed and potential applications to EEG will be discussed.
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 CARMA COLLOQUIUM
 Speaker: Michael Whittaker , University of Wollongong
 Title: Fractal substitution tilings and applications to noncommutative geometry
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 14^{th} May 2015
 Abstract:
Starting with a substitution tiling, such as the Penrose
tiling, we demonstrate a method for constructing infinitely many new
substitution tilings. Each of these new tilings is derived from a
graph iterated function system and the tiles typically have fractal
boundary. As an application of fractal tilings, we construct an odd
spectral triple on a C*algebra associated with an aperiodic
substitution tiling. Even though spectral triples on substitution
tilings have been extremely well studied in the last 25 years, our
construction produces the first truly noncommutative spectral triple
associated with a tiling. My work on fractal substitution tilings is
joint with Natalie Frank and Sam Webster, and my work on spectral
triples is joint with Michael Mampusti.
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 CARMA COLLOQUIUM
 Speaker: Andy Hammerlindl, University of NSW
 Title: Geometry and Dynamics
 Location: Room V102, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Wed, 11^{th} Mar 2015
 Abstract:
Consider a function from the circle to itself such that the derivative
is greater than one at every point.
Examples are maps of the form f(x) = mx for integers m > 1. In some
sense, these are the only possible examples. This fact and the
corresponding question for maps on higher dimensional manifolds was a
major motivation for Gromov to develop pioneering results in the field
of geometric group theory.
In this talk, I'll give an overview of this and other results relating
dynamical systems to the geometry of the manifolds on which they act
and (time permitting) talk about my own work in the area.
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 CARMA COLLOQUIUM
 Speaker: Stephan Harrap, Department of Mathematical Sciences, Durham University
 Title: Topological games, Cantor sets and Diophantine approximation: An introduction
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 5^{th} Mar 2015
 Abstract:
When attacking various difficult problems in the field of Diophantine approximation the application of certain topological games has proven extremely fruitful in recent times due to the amenable properties of the associated 'winning' sets. Other problems in Diophantine approximation have recently been solved via the method of constructing certain treelike structures inside the Diophantine set of interest. In this talk I will discuss how one broad method of treelike construction, namely the class of 'generalised Cantor sets', can be formalized for use in a wide variety of problems. By introducing a further class of socalled 'Cantorwinning' sets we may then provide a criterion for arbitrary sets in a metric space to satisfy the desirable properties usually attributed to winning sets, and so in some sense unify the two above approaches. Applications of this new framework include new answers to questions relating to the mixed Littlewood conjecture and the $\times2, \times3$ problem. The talk will be aimed at a broad audience.
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 CARMA COLLOQUIUM
 Speaker: William McLean, University of NSW
 Title: Error bounds for time stepping of fractional diffusion equations with nonsmooth initial data
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 18^{th} Dec 2014
 Abstract:
We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform techniques, we show that the method is first order accurate at the $n$th time level~$t_n$, but the error bound includes a factor~$t_n^{1}$ if we assume no smoothness of the initial data. We also show that for smoother initial data the growth in the error bound for decreasing time is milder, and in some cases absent altogether. Our error bounds generalize known results for the classical heat equation and are illustrated using a model 1D problem.
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 CARMA LECTURE
 Speaker: José Burillo, Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya
 Title: Lectures on Thompson's groups  final
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Dates: Mon, 3^{rd} Nov 2014  Mon, 3^{rd} Nov 2014
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 CARMA COLLOQUIUM
 Speaker: Dr Mike Meylan, CARMA, The University of Newcastle
 Title: Wave Scattering in the Marginal Ice Zone
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 9^{th} Oct 2014
 Abstract:
One of the key components in the earth’s climate is the formation and melting of sea ice. Currently, we struggle to model correctly this process. One possible explanation for this shortcoming is that ocean waves play a key role and that their effect needs to be include in climate models. I will describe a series of recent experiments which seem to validate this hypothesis and discuss attempts my myself and others to model waveice interaction.
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 CARMA COLLOQUIUM
 Speaker: Guoyin Li, University of NSW
 Title: Some Recent Advances of Polynomial Optimization: going back and forth between the "polynomial world'' and the "convexity world''
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 2^{nd} Oct 2014
 Abstract:
Optimization problems involving polynomial functions are of great importance in applied mathematics and engineering, and they are intrinsically hard problems. They arise in important engineering applications such as the sensor network localization problem, and provide a rich and fruitful interaction between algebraicgeometric concepts and modern convex programming (semidefinite programming). In this talk, we will discuss some recent progress of the polynomial (semialgebraic) optimization with a focus on the intrinsic link between the polynomial structure and the hidden convexity structure. The talk will be divided into two parts. In the first part, we will describe the key results in this new area, highlighting the geometric and conceptual aspects as well as recent work on global optimality theory, algorithms and applications. In the second part, we will explain how the semialgebraic structure helps us to analyze some important and classical algorithms in optimization such as alternating projection algorithm, proximal point algorithm and DouglasRachford algorithm (if time is permitted).
 [Permanent event link]
 CARMA LECTURE
 Speaker: José Burillo, Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya
 Title: Lectures on Thompson’s group F
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Dates: Mon, 22^{nd} Sep 2014  Mon, 22^{nd} Sep 2014
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof. George Willis, CARMA, The University of Newcastle
 Title: Functions on groups
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 11^{th} Sep 2014
 Abstract:
The topological and measure structures carried by locally compact groups make them precisely the class of groups to which the methods of harmonic analysis extend. These methods involve study of spaces of real or complexvalued functions on the group and general theorems from topology guarantee that these spaces are sufficiently large. When analysing particular groups however, particular functions deriving from the structure of the group are at hand. The identity function in the cases of $(\mathbb{R},+)$ and $(\mathbb{Z},+)$ are the most obvious examples, and coordinate functions on matrix groups and growth functions on finitely generated discrete groups are only slightly less obvious.
In the case of totally disconnected groups, compact open subgroups are essential structural features that give rise to positive integervalued functions on the group. The set of values of $p$ for which the reciprocals of these functions belong to $L^p$ is related to the structure of the group and, when they do, the $L^p$norm is a type of $\zeta$function of $p$. This is joint work with Thomas Weigel of Milan.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Volker Diekert, University of Stuttgart
 Title: Finding all solutions of equations in free groups and monoids with involution
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 14^{th} Aug 2014
 Abstract:
We present a PSPACEalgorithm to compute a finite graph of exponential
size that describes the set of all solutions of equations in free
groups with rational constraints. This result became possible due to
the recently invented recompression technique of Artur Jez. We show
that it is decidable in PSPACE whenever the set of all solutions is
finite. If the set of all solutions is finite, then the length of a
longest solution is at most doubly exponential.
This talk is based on a joint paper with Artur Jez and Wojciech
Plandowski (arXiv:1405.5133 and LNCS 2014, Proceedings CSR 2014, Moscow, June 7  11, 2014).
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Jerome Droniou, Monash University
 Title: Numerical schemes for diffusion equations: how to construct them, and how to analyse their convergence under realworld constraints
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Wed, 23^{rd} Jul 2014
 Abstract:
A vast amount of natural processes can be modelled by
partial differential equations involving diffusion operators.
The NavierStokes equations of fluid dynamics is one of the most
popular of such models, but many other equations describing
flows involve diffusion processes.
These equations are often nonlinear and coupled, and theoretical
analysis can only provided limited information on the qualitative
behaviours of their solutions. Numerical analysis is then used to
obtain a prediction of the fluid's behaviour.
In many circumstances, the numerical methods used to approximate the
models must satisfy engineering or computational constraints. For
examples, in underground flows in porous media (involved in oil
recovery, carbon storage or hydrogeology), the diffusions properties
of the medium vary a lot between geological layers, and can be
strongly skewed in one direction. Moreover, the available meshes
used to discretise the equations may be quite irregular. The sheer
size of the domain of study (a few kilometres wide) also calls for
methods that can be easily parallelised and give good and stable
results on relatively large grids. These constraints make the construction
and study of numerical methods for diffusion models very challenging.
In the first part of this talk, I will present some numerical schemes,
developed in the last 10 years and designed to discretise diffusion
equations as encountered in reservoir engineering, with all the
associated constraints. In the second part, I will focus
on mathematical tools and techniques constructed to analyse the
convergence of numerical schemes under realistic hypotheses (i.e.
without assuming nonphysical smoothness on the data or the solutions).
These techniques are based on the adaptation to the discrete setting
of functional analysis results used to study the continuous equations.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Joydeep Dutta, Department of Mathematics and Statistics, Indian Institute of Technology Kanpur
 Title: The Problem of Lagrange and other stories from the calculus of variations
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 5^{th} Jun 2014
 Abstract:
We begin the talk with the story of Dido and the Brachistochrone problem. We show how these two problems leads to the two must fundamental problems of the calculus of variations. The Brachistochrone problem leads to the basic problem of calculus of variations and that leads to the EulerLagrange equation. We show the link between the EulerLagrange equations and the laws of classical mechanics.
We also discuss about the Legendre conditions and Jacobi conjugate points which leads to the sufficient conditions for weak local minimum points .
The Dido's problem leads to the problem of Lagrange in which Lagrange introduces his multiplier rule. We also speak a bit about the problem of Bolza and further also discuss about how the class of extremals can be enlarged and the issue of existence of solutions in calculus of variations, the Tonelli's direct methods and some more facts on the quest for multiplier rules.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
 Title: Experimental Computation and Visual Theorems: Part II
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 29^{th} May 2014
 Abstract:
In these two talks chapter I want to talk, both generally and personally, about the use of tools in the practice of modern research mathematics. To focus my attention I have decided to discuss the way I and my research group members have used tools primarily computational (visual, numeric and symbolic) during the past five years. When the tools are relatively accessible I shall exhibit details; when they are less accessible I settle for illustrations and discussion of process.
Long before current graphic, visualisation and geometric tools were available, John E. Littlewood, 18851977, wrote in his delightful Miscellany:
A heavy warning used to be given [by lecturers] that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety. Some pictures, of course, are not rigorous, but I should say most are (and I use them whenever possible myself).
Over the past five years, the role of visual computing in my own research has expanded dramatically. In part this was made possible by the increasing speed and storage capabilities  and the growing ease of programming  of modern multicore computing environments. But, at least as much, it has been driven by paying more active attention to the possibilities for graphing, animating or simulating most mathematical research activities.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
 Title: Experimental Computation and Visual Theorems: Part I
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Wed, 21^{st} May 2014
 Abstract:
In these two talks chapter I want to talk, both generally and personally, about the use of tools in the practice of modern research mathematics. To focus my attention I have decided to discuss the way I and my research group members have used tools primarily computational (visual, numeric and symbolic) during the past five years. When the tools are relatively accessible I shall exhibit details; when they are less accessible I settle for illustrations and discussion of process.
Long before current graphic, visualisation and geometric tools were available, John E. Littlewood, 18851977, wrote in his delightful Miscellany:
A heavy warning used to be given [by lecturers] that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety. Some pictures, of course, are not rigorous, but I should say most are (and I use them whenever possible myself).
Over the past five years, the role of visual computing in my own research has expanded dramatically. In part this was made possible by the increasing speed and storage capabilities  and the growing ease of programming  of modern multicore computing environments. But, at least as much, it has been driven by paying more active attention to the possibilities for graphing, animating or simulating most mathematical research activities.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Jennifer Badham, University of Surrey
 Title: Personal Protective Behaviour During an Epidemic
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Wed, 16^{th} Apr 2014
 Abstract:
The TELL ME agent based model will simulate personal protective decisions such as vaccination or hand hygiene during an influenza epidemic. Such behaviour may be adopted in response to communication from health authorities, taking into account perceived influenza risk. The behaviour decisions are to be modelled with a combination of personal attitude, average local attitude, the local number of influenza cases and the case fatality rate. The model is intended to be used to understand the effects of choices about how to communicate with citizens about protecting themselves from epidemics. I will discuss the TELL ME model design, the cognitive theory supporting the design and some of the expected problems in building the simulation.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Judyanne Osborn, CARMA, The University of Newcastle
 Title: Tipping the balance towards scientific thinking, via zombies and maths
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 27^{th} Feb 2014
 Abstract:
Brad Pitt's zombieattack movie "World War Z" may not seem like a natural jumpingoff point for a discussion of mathematics or science, but in fact it was a request I received to review that movie in "The Conversation" and the review I wrote that led me to be invited to give a public lecture on zombies and maths at the Academy of Science next week. This week's colloquium will largely be a preview of that talk, so should be generally accessible.
My premise is that movies and maths have something in common. Both enable a trait which seems to be more highly developed in humans than in any other species, with profound consequences: the desire and capacity to explore possibilityspace.
The same mathematical models can let us playfully explore how an outbreak of zombieism might play out, or how an outbreak of an infectious disease like measles would spread, depending, in part, on what choices we make. Where a movie gives us deep insight into one possibility, mathematics enables us to explore, at all once, millions of scenarios, and see where the critical differences lie.
I will try to use mathematical models of zombie outbreak to discuss how mathematical modelling and mathematical ideas such as functions and phase transitions might enter the public consciousness in a positive way.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Jonathan Kress, University of NSW
 Title: Coupling constant metamorphosis and conformally covariant Laplacians
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Wed, 12^{th} Feb 2014
 Abstract:
This talk will give an introduction to the KelperCoulomb and harmonic oscillator systems fundamental in both the classical and quantum worlds. These systems are related by "coupling constant metamorphosis", a remarkable trick that exchanges the energy of one system with the coupling constant of the other. The trick can be seen to be a type of conformal transformation, that is, a scaling of the underlying metric, that maps "conformal symmetries" to "true symmetries" of a Hamiltonian system.
In this talk I will explain the explain the statements above and discuss some applications of coupling constant metamorphosis to superintegrable systems and differential geometry.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof. George Willis, CARMA, The University of Newcastle
 Title: Amenability, measure and randomness in groups
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 4:00 pm, Thu, 28^{th} Nov 2013
 Abstract:
This colloquium will explain some of the background and significance of the concept of amenability. Arguments with finite groups frequently, without remark, count the number of elements in a subset or average a function over the group. It is usually important in these arguments that the result of the calculation is invariant under translation. Such calculations cannot be so readily made in infinite groups but the concepts of amenability and translation invariant measure on a group in some ways take their place. The talk will explain this and also say how random walks relate to these same ideas.
The link to the animation of the paradoxical decomposition is here.
 Download: Colloquium presentation (136 KB)
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Ali Eshragh, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Binomial Observations, Fisher Information and Optimal Sampling Times
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 14^{th} Nov 2013
 Abstract:
Our goal is to estimate the rate of growth of a population governed by a simple stochastic model. We may choose (n) sampling times at which to count the number of individuals present, but due to detection difficulties, or constraints on resources, we are able only to observe each individual with fixed probability (p). We discuss the optimal sampling times at which to make our observations in order to approximately maximize the accuracy of our estimation. To achieve this, we maximize the expected volume of information obtained from such binomial observations, that is the Fisher Information. For a single sample, we derive an explicit form of the Fisher Information. However, finding the Fisher Information for higher values of (n) appears intractable. Nonetheless, we find a very good approximation function for the Fisher Information by exploiting the probabilistic properties of the underlying stochastic process and developing a new class of delayed distributions. Both numerical and theoretical results strongly support this approximation and confirm its high level of accuracy.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Andrew Rechnitzer, UBC
 Title: Counting knots
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 31^{st} Oct 2013
 Abstract:
Recently a great deal of attention from biologists has been
directed to understanding the role of knots in perhaps the most
famous of long polymers  DNA. In order for our cells to
replicate, they must somehow untangle the approximately
two metres of DNA that is packed into each nucleus. Biologists
have shown that DNA of various organisms is nontrivially
knotted with certain topologies preferred over others. The
aim of our work is to determine the "natural" distribution of
different knottypes in random closed curves and compare that
to the distributions observed in DNA.
Our tool to understand this distribution is a canonical model
of long chain polymers  selfavoiding polygons (SAPs). These
are embeddings of simple closed curves into a regular lattice.
The exact computation of the number of polygons
of length n and fixed knot type K is extremely difficult
 indeed the current best algorithms can barely touch the
first knotted polygons. Instead of exact methods, in this
talk I will describe an approximate enumeration method  which
we call the GAS algorithm. This is a generalisation of the famous
Rosenbluth method for simulating linear polymers. Using this
algorithm we have uncovered strong evidence that the limiting
distribution of different knottypes is universal. Our data shows
that a long closed curve is about 28 times more likely to be a
trefoil than a figureeight, and that the natural distribution
of knots is quite different from those found in DNA.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Sheehan Olver, The University of Sydney
 Title: Numerical Random Matrix Theory
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 12^{th} Sep 2013
 Abstract:
Random matrix theory has undergone significant theoretical progress in the last two decades, including proofs on universal behaviour of eigenvalues as the matrix dimension becomes large, and a deep connection between algebraic manipulations of random matrices and free probability theory. Underlying many of the analytical advances are tools from complex analysis. By developing numerical versions of these tools, it is now possible to calculate random matrix statistics to high accuracy, leading to new conjectures on the behaviour of random matrices. We overview recent advances in this direction.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle
 Title: Incremental network design for minimum spanning trees
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 29^{th} Aug 2013
 Abstract:
(Joint work with Konrad Engel and Martin Savelsbergh)
In an incremental network design problem we want to expand an existing network over several time periods, and we are interested in some quality measure for all the intermediate stages of the expansion process. In this talk, we look at the following simple variant: In each time period, we are allowed to add a single edge, the cost of a network is the weight of a minimum spanning tree, and the objective is to minimize the sum of the costs over all time periods. We describe a greedy algorithm for this problem and sketch a proof of the fact that it provides an optimal solution. We also indicate that incremental versions of other basic network optimization problems (shortest path and maximum flow) are NPhard.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Colin Reid, CARMA, The University of Newcastle
 Title: Locally normal subgroups of totally disconnected groups
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 1^{st} Nov 2012
 Abstract:
I will give an extended version of my talk at the AustMS meeting about some ongoing work with PierreEmmanuel Caprace and George Willis.
Given a locally compact topological group G, the connected component of the identity is a closed normal subgroup G_0 and the quotient group is totally disconnected. Connected locally compact groups can be approximated by Lie groups, and as such are relatively wellunderstood. By contrast, totally disconnected locally compact (t.d.l.c.) groups are a more difficult class of objects to understand. Unlike in the connected case, it is probably hopeless to classify the simple t.d.l.c. groups, because this would include for instance all simple groups (equipped with the discrete topology). Even classifying the finitely generated simple groups is widely regarded as impossible. However, we can prove some general results about broad classes of (topologically) simple t.d.l.c. groups that have a compact generating set.
Given a nondiscrete t.d.l.c. group, there is always an open compact subgroup. Compact totally disconnected groups are residually finite, so have many normal subgroups. Our approach is to analyse a t.d.l.c. group G (which may itself be simple) via normal subgroups of open compact subgroups. From these we obtain lattices and Cantor sets on which G acts, and we can use properties of these actions to demonstrate properties of G. For instance, we have made some progress on the question of whether a compactly generated topologically simple t.d.l.c. group is abstractly simple, and found some necessary conditions for G to be amenable.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Brandon Turner, Stanford University
 Title: ABCDE: A practical likelihoodfree Bayesian analysis technique with applications to mathematical models of cognition
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Wed, 24^{th} Oct 2012
 Abstract:
Many cognitive models derive their predictions through simulation. This means that it is difficult or impossible to write down a probability distribution or likelihood that characterizes the random behavior of the data as a function of the model's parameters. In turn, the lack of a likelihood means that standard Bayesian analyses of such models are impossible. In this presentation we demonstrate a procedure called approximate Bayesian computation (ABC), a method for Bayesian analysis that circumvents the evaluation of the likelihood. Although they have shown great promise for likelihoodfree inference, current ABC methods suffer from two problems that have largely revented their mainstream adoption: long computation time and an inability to scale beyond models with few parameters. We introduce a new ABC algorithm, called ABCDE, that includes differential evolution as a computationally efficient genetic algorithm for proposal generation. ABCDE is able to obtain accurate posterior estimates an order of magnitude faster than a popular rejectionbased method and scale to highdimensional parameter spaces that have proven difficult for the current rejectionbased ABC methods. To illustrate its utility we apply ABCDE to several wellestablished simulationbased models of memory and decisionmaking that have never been fit in a Bayesian framework.
AUTHORS: Brandon M. Turner (Stanford University) Per B. Sederberg (The Ohio State University)
 [Permanent event link]
 CARMA COLLOQUIUM
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 11^{th} Oct 2012
 This is an attempt to restart informal shared problem sessions (with lollipops as rewards). It is intended for brief presentations where you hope others can help with, or comment usefully, on one of your research questions. Please prepare one or two overheads or come ready to speak at the board.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
 Title: Interdisciplinarity, Innovation, Collaboration and Creativity or How to Manage a Research Portfolio
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 13^{th} Sep 2012
 Abstract:
I will discuss four much abused words Interdisciplinarity, Innovation, Collaboration and Creativity. I will describe what they mean for different stakeholder groups and will speak about my own experiences as a research scientist, as a scientific administrator, as an educator and even as a small hightech businessman. I will also offer advice that can of course be ignored.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof A. Bass Bagayogo, Université de SaintBoniface
 Title: Applied Special Functions for Geohydrology Problems
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 23^{rd} Aug 2012
 Abstract:
Groundwater makes up nearly 30% of the entire world’s freshwater but the mathematical models for the better understanding of the system are difficult to validate due to the disordered nature of the porous media and the complex geometry of the channels of flow. In this seminar, after establishing the statistical macroscopic equivalent of the NavierStokes equations for the groundwater hydrodynamic and its consequences in term of Laplace and diffusion equations, some cases will be solved in term of special functions by using the modern Computer Algebra System.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Michael Coons, CARMA, The University of Newcastle
 Title: A functional introduction to Mahler's method
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 9^{th} Aug 2012
 Abstract:
Let $F(z)$ be a power series, say with integer coefficients. In the late 1920s and early 1930s, Kurt Mahler discovered that for $F(z)$ satisfying a certain type of functional equation (now called Mahler functions), the transcendence of the function $F(z)$ could be used to prove the transcendence of certain special values of $F(z)$. Mahler's main application at the time was to prove the transcendence of the ThueMorse number $\sum_{n\geq 0}t(n)/2^n$ where $t(n)$ is either 0 or 1 depending on the parity of the number of 1s in the base 2 expansion of $n$. In this talk, I will talk about some of the connections between Mahler functions and finite automata and highlight some recent approaches to large problems in the area. If time permits, I will outline a new proof of a version of Carlson's theorem for Mahler functions; that is, a Mahler function is either rational or it has the unit circle as a natural boundary.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof John Giles, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: On a Weakly Uniformly Rotund Dual of a Banach Space
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 26^{th} Jul 2012
 Abstract:
Hajek proved that a WUR Banach space is an Asplund space. This result suggests that the WUR property might have interesting consequences as a dual property. We show that
(i) every Banach Space with separable second dual can be equivalently renormed to have WUR dual,
(ii) under certain embedding conditions a Banach space with WUR dual is reflexive.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
 Title: Three approaches to linear mean iterations
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 5^{th} Jul 2012
 Abstract:
Motivated by questions of algorithm analysis, we provide several distinct approaches to determining convergence and limit values for a class of linear iterations.
This is joint work with D. Borwein and B. Sims.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Robert Corless, University of Western Ontario
 Title: First Encounters of a Chebfun Novice
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 1:00 pm, Tue, 3^{rd} Apr 2012
 Abstract:
Symbolic and numeric computation have been distinguished by definition: numeric computation puts numerical values in its variables as soon as possible, symbolic computation as late as possible. Chebfun blurs this distinction, aiming for the speed of numerics with the generality and flexibility of symbolics. What happens when someone who has used both Maple and Matlab for decades, and has thereby absorbed the different fundamental assumptions into a "computational stance", tries to use Chebfun to solve a variety of computational problems? This talk reports on some of the outcomes.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Zdenek Ryjacek, ITI Research Centre, KMA, University of West Bohemia, Pilsen
 Title: Closure techniques for cycles and paths in graphs
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 9^{th} Feb 2012
 Abstract:
Graph closures became recently an important tool in Hamiltonian Graph Theory since the use of closure techniques often substantially simplifies the structure of a graph under consideration while preserving some of its prescribed properties (usually of Hamiltonian type). In the talk we show basic ideas of construction of some graph closures for clawfree graphs and techniques that allow to reduce the problem to cubic graphs. The approach will be illustrated on a recently introduced closure concept for Hamiltonconnectedness in clawfree graphs and, as an application, an asymptotically sharp Oretype degree condition for Hamiltonconnectedness in clawfree graphs will be obtained.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
 Title: Advanced Collaborative Environments
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 3^{rd} Nov 2011
 Abstract:
I shall describe highlights of my two decades of experience with Advanced Collaborative Environments (ACEs) in Canada and Australia, running shared seminars, conferences, resources and courses over the internet. I shall also describe the AMSI Virtual Lab proposal which has just been submitted to NeCTAR. The slides for much of this talk are at http://www.carma.newcastle.edu.au/jon/aces11.pdf.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Philip Laird, University of Wollongong
 Title: Mean Periodic Functions and Mean Value Theorems
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 20^{th} Oct 2011
 Abstract:
Mean periodic functions of a single real variable were an innovation of the mid20th century. Although not as well known as almost periodic functions, they have some nice properties, with applications to certain mean value theorems.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Amnon Neeman, Mathematical Sciences Institute, Australian National University
 Title: From CompactlyGenerated to WellGenerated Triangulated Categories
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 13^{th} Oct 2011
 Abstract:
The talk will begin with a reminder of what a triangulated category is, the context in which they arose, and why we care about them. Then we will discuss the theory of compactly generated triangulated categories, again illustrating the applications. This theory is old and well understood. Finally we will come to well generated categories, where several open problems remain very mysterious.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof. Dr. habil. Matthias Ehrgott, Department of Engineering Science, The University of Auckland
 Title: A MultiPlan Method for Radiotherapy Treatment Design via Finite Representation of the NonDominated Set of a MultiObjective Linear Programme
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Fri, 30^{th} Sep 2011
 Abstract:
The choice of a plan for radiotherapy treatment for an individual cancer patient requires the careful tradeoff between the goals of delivering a sufficiently high radiation dose to the tumour and avoiding irradiation of critical organs and normal tissue. This problem can be formulated as a multiobjective linear programme (MOLP). In this talk we present a method to compute a finite set of nondominated points that can be proven to uniformly cover the complete nondominated set of an MOLP (a finite representation). This method generalises and improves upon two existing methods from the literature. We apply this method to the radiotherapy treatment planning problem, showing some results for clinical cases. We illustrate how the method can be used to support clinician’s decision making when selecting a treatment plan. The treatment planner only needs to specify a threshold for recognising two treatment plans as different and is able to interactively navigate through the representative set without the trialanderror process often used in practice today.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Rafa Espinola, Department of Mathematical Analysis, University of Seville
 Title: Ptolemy vs. CAT(0) spaces
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 15^{th} Sep 2011
 Abstract:
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). If the quadrilateral is given with its four vertices $A$, $B$, $C$, and $D$ in order, then the theorem states that:
$$AC \cdot BD = AB \cdot CD + AD \cdot BC.$$
Furthermore, it is well known that in every Euclidean (or Hilbert) space $H$ we have that
$$x  y \cdot z  w \leq x  z \cdot y  w + z  y \cdot x  w$$
for any four points $w, x, y, z \in H$. This is the classical Ptolemy inequality and it is wellknown that it characterizes the inner product spaces among all normed spaces. A Ptolemy metric space is any metric space for which the same inequality holds, replacing norms by distances, for any four points.
CAT(0) spaces are geodesic spaces of global nonpositive curvature in the sense of Gromov. Hilbert spaces are CAT(0) spaces and, even more, CAT(0) spaces have many common properties with Hilbert spaces. In particular, although a Ptolemy geodesic metric space need not be CAT(0), any CAT(0) space is a Ptolemy metric space. In this expository talk we will show some recent progress about the connection between Ptolemy metric spaces and CAT(0) spaces.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
 Title: Stack sorting and patternavoiding permutations
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 18^{th} Aug 2011
 Abstract:
Given a mixedup sequence of distinct numbers, say 4 2 1 5 7 3 6, can you pass them through an infinite stack (firstinlastout) from right to left, and put them in order?
2 1 5 7 3 6
 
 4 
___
1 5 7 3 6
 
 2 
 4 
___
1 5 7 3 6
 
 2 
 4 
___
1 2 5 7 3 6
 
 4 
___
umm…..
This talk will be about this problem  when can you do it with one stack, two stacks (in series), an infinite and a finite capacity stack in series, etc etc? How many permutations of 1,2,...,n are there that can be sorted?
The answer will lie in the "forbidden subpatterns" of permutations, and it turns out there is a whole theory of this, which I will try to describe.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
 Title: Odds of Riemann's zeta function
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 4^{th} Aug 2011
 Abstract:
In my talk I will try to overview ideas behind (still recent)
achievements on arithmetic properties of numbers
$\zeta(s)=\sum_{n=1}^\infty n^{s}$ for integral $s\ge2$,
with more emphasis on odd $s$. The basic ingredients of
proofs are generalized hypergeometric functions and
linear independence criteria. I will also address some
"most recent" results and observations in the subject,
as well as connections with other problems in number theory.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof David Bailey, Berkeley, California
 Title: HandtoHand Combat with ThousandDigit Integrals
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 12:00 pm, Fri, 22^{nd} Jul 2011
 Abstract:
One of the most effective avenues in recent experimental mathematics research is the computational of definite integrals to high precision, followed by the identification of resulting numerical values as compact analytic formulas involving wellknown constants and functions. In this talk we summarize several applications of this methodology in the realm of applied mathematics and mathematical physics, in particular Ising theory, "box integrals", and the study of random walks.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Boris Mordukhovich, Department of Mathematics, Wayne State University
 Title: Generalized Newton's method based on graphical derivatives
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 21^{st} Jul 2011
 Abstract:
This talk concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newtontype method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the wellposedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness and Lipschitzian assumptions, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with wellrecognized semismooth and $B$differentiable versions of Newton's method for nonsmooth Lipschitzian equations.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Ross McPhedran, The University of Sydney
 Title: The Riemann Hypothesis for Combinations of Zeta Functions
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 14^{th} Jul 2011
 Abstract:
This paper studies combinations of the Riemann zeta function, based on one defined by P.R. Taylor, and shown by him to have all its zeros on the critical line. With a rescaled complex argument, this is denoted here by ${\cal T}_(s)$, and is considered together with a counterpart function ${\cal T}_+(s)$, symmetric rather than antisymmetric about the critical line. We prove by a graphical argument that ${\cal T}_+(s)$ has all its zeros on the critical line, and that the zeros of both functions are all of first order. We also establish a link between the zeros of ${\cal T}_(s)$ and of ${\cal T}_+s)$ with zeros of the Riemann zeta function $\zeta(2 s1)$, and between the distribution functions of the zeros of the three functions.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Josef Dick, School of Mathematics and Statistics, University of NSW
 Title: Highdimensional Numerical Integration
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 16^{th} Jun 2011
 Abstract:
Highdimensional integrals come up in a number of applications like statistics, physics and financial mathematics. If explicit solutions are not known, one has to resort to approximative methods. In this talk we will discuss equalweight quadrature rules called quasiMonte Carlo. These rules are defined over the unit cube $[0,1]^s$ with carefully chosen quadrature points. The quadrature points can be obtained using numbertheoretic and algebraic methods and are designed to have low discrepancy, where discrepancy is a measure of how uniformly the quadrature points are distributed in $[0,1]^s$. In the onedimensional case, the discrepancy coincides with the KolmogorovSmirnov distance between the uniform distribution and the empirical distribution of the quadrature points and has also been investigated in a paper by Weyl published in 1916.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Camilla Hollanti, Department of Mathematics, University of Turku
 Title: An Algebraic Approach to Digital Broadcasting
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 26^{th} May 2011
 Abstract:
The aim of this talk is to demonstrate how cyclic division algebras and their orders can be used to enhance wireless communications. This is done by embedding the information bits to be transmitted into smart algebraic structures, such as matrix representations of order lattices. We will recall the essential algebraic definitions and structures, and further familiarize the audience with the transmission model of fading channels. An example application of major current interest is digital video broadcasting. Examples suitable to this application will be provided.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Stephan Tillman, School of Mathematics and Physics, The University of Queensland
 Title: What is the Thurston norm?
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 19^{th} May 2011
 Abstract:
In the late seventies, Bill Thurston defined a seminorm on the homology of a 3dimensional manifold which lends itself to the study of manifolds which fibre over the circle. This led him to formulate the Virtual Fibration Conjecture, which is fairly inscrutable and implies almost all major results and conjectures in the field. Nevertheless, Thurston gave the conjecture "a definite chance for a positive answer" and much research is currently devoted to it. I will describe the Thurston norm, its main properties and applications, as well as its relationship to McMullen’s Alexander norm and the geometric invariant for groups due to Bieri, Neumann and Strebel.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Adam Piggott, Department of Mathematics, Bucknell University
 Title: Palindromic automorphisms of free groups
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 5^{th} May 2011
 Abstract:
The elements of a free group are naturally considered to be reduced "words" in an certain alphabet. In this context, a palindrome is a group element which reads the same from lefttoright and righttoleft. Certain primitive elements, elements that can be part of a basis for the free group, are palindromes. We discuss these elements, and related automorphisms.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Sean Dineen, School of Mathematical Sciences, University College Dublin
 Title: An Introduction to Monomial Expansions in Infinitely Many Variables
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 28^{th} Apr 2011
 Abstract:
We introduce, assuming only a modest background in one variable complex
analysis, the rudiments of infinite dimensional holomorphy. Approaches and
some answers to elementary questions arising from considering monomial
expansions in different settings and spaces are used to sample the subject.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: , CARMA, The University of Newcastle
 Title: CDSCCARMACISRA afternoon
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 12:00 pm, Wed, 20^{th} Apr 2011
 Abstract:
On wednesday afternoon, we will be visited by Dr Stephen Hardy and Dr Kieran Larkin from Canon Information Systems Research Australia, Sydney. Drs Larkin and Hardy will be here to explore research opportunities with University of Newcastle researchers. To familiarise them with what we do and to help us understand what they do, there will be three short talks, giving information on the functions and activities of the CDSC, CARMA and Canon's group of 45 researchers. All are welcome to participate.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Heinz Bauschke, Mathematics and Statistics, UBC Okanagan
 Title: New Demiclosedness Principles for (Firmly) Nonexpansive Operators
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: IRMACS Room
 Time and Date: 9:30 am, Thu, 14^{th} Apr 2011
 Abstract:
The demiclosedness principle is one of the key tools in nonlinear analysis and fixed point theory. In this talk, this principle is extended and made more flexible by two mutually orthogonal affine subspaces. Versions for finitely many (firmly) nonexpansive operators are presented. As an application, a simple proof of the weak convergence of the DouglasRachford splitting algorithm is provided.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Michael Kozdron, Department of Mathematics & Statistics , University of Regina
 Title: A Random Look at the SchrammLoewner Evolution
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:30 pm, Thu, 7^{th} Apr 2011
 Abstract:
The stochastic Loewner evolution (SLE) is a oneparameter family of random
growth processes in the complex plane introduced by the late Oded Schramm in
1999 which is predicted to describe the scaling limit of a variety of
statistical physics models. Recently a number of rigorous results about such
scaling limits have been established; in fact, Wendelin Werner was awarded the
Fields Medal in 2006 for "his contributions to the development of stochastic
Loewner evolution, the geometry of twodimensional Brownian motion, and
conformal field theory" and Stas Smirnov was awarded the Fields Medal in 2010
"for the proof of conformal invariance of percolation and the planar Ising
model in statistical physics." In this talk, I will introduce some of these
models including the Ising model, selfavoiding walk, looperased random walk,
and percolation. I will then discuss SLE, describe some of its basic
properties, and touch on the results of Werner and Smirnov as well as some of
the major open problems in the area. This talk will be "colloquium style" and
is intended for a general mathematics audience.
 Please note the variation from our usual colloquium time.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
 Title: Life of Pi: History and Computation
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 10:00 am, Tue, 15^{th} Mar 2011
 Download: Presentation (25 MB)
 Abstract:
Professor Jonathan Borwein shares with us his passion for \(\pi\), taking us on a journey through its rich history.
Professor Borwein begins with approximations of \(\pi\) by ancient cultures, and leads us through the work of Archimedes, Newton and others to the calculation of \(\pi\) in today's age of computers.
Professor Borwein is currently Laureate Professor in the School of Mathematical and Physical Sciences at the University of Newcastle. His research interests are broad, spanning pure, applied and computational mathematics and highperformance computing. He is also Chair of the Scientific Advisory Committee at the Australian Mathematical Sciences Institute (AMSI).
This talk will be broadcast from the Access Grid room V206 at the University of Newcastle, and will link to the West coast of Canada.
For more information visit AMSI's Pi Day website or read Jon Borwein's talk.
 Download: Presentation (25 MB)
 [Permanent event link]
 CARMA COLLOQUIUM AND SIGMAOPT SEMINAR
 Speaker: Qiji Jim Zhu, Department of Mathematics, Western Michigan University
 Title: Why Bankers Should Learn Convex Analysis. (Part 2)
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 11:00 am, Fri, 4^{th} Mar 2011
 Abstract:
Concave utility functions and convex risk measures play crucial roles in economic and financial problems. The use of concave utility function can at least be traced back to Bernoulli when he posed and solved the St. Petersburg wager problem. They have been the prevailing way to characterize rational market participants for a long period of time until the 1970’s when Black and Scholes introduced the replicating portfolio pricing method and Cox and Ross developed the risk neutral measure pricing formula. For the past several decades the `new paradigm’ became the main stream. We will show that, in fact, the `new paradigm’ is a special case of the traditional utility maximization and its dual problem. Moreover, the convex analysis perspective also highlights that overlooking sensitivity analysis in the `new paradigm’ is one of the main reason that leads to the recent financial crisis. It is perhaps time again for bankers to learn convex analysis.
The talk will be divided into two parts. In the first part we layout a discrete model for financial markets. We explain the concept of arbitrage and the no arbitrage principle. This is followed by the important fundamental theorem of asset pricing in which the no arbitrage condition is characterized by the existence of martingale (risk neutral) measures. The proof of this gives us a first taste of the importance of convex analysis tools. We then discuss how to use utility functions and risk measures to characterize the preference of market agents. The second part of the talk focuses on the issue of pricing financial derivatives. We use simple models to illustrate the idea of the prevailing Black Scholes replicating portfolio pricing method and related CoxRoss riskneutral pricing method for financial derivatives. Then, we show that the replicating portfolio pricing method is a special case of portfolio optimization and the risk neutral measure is a natural byproduct of solving the dual problem. Taking the convex analysis perspective of these methods h
 Download: Presentation (1.3 MB)
 [Permanent event link]
 CARMA COLLOQUIUM AND SIGMAOPT SEMINAR
 Speaker: Qiji Jim Zhu, Department of Mathematics, Western Michigan University
 Title: Why Bankers Should Learn Convex Analysis (Part 1)
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 11:00 am, Thu, 3^{rd} Mar 2011
 Abstract:
Concave utility functions and convex risk measures play crucial roles in economic and financial problems. The use of concave utility function can at least be traced back to Bernoulli when he posed and solved the St. Petersburg wager problem. They have been the prevailing way to characterize rational market participants for a long period of time until the 1970’s when Black and Scholes introduced the replicating portfolio pricing method and Cox and Ross developed the risk neutral measure pricing formula. For the past several decades the `new paradigm’ became the main stream. We will show that, in fact, the `new paradigm’ is a special case of the traditional utility maximization and its dual problem. Moreover, the convex analysis perspective also highlights that overlooking sensitivity analysis in the `new paradigm’ is one of the main reason that leads to the recent financial crisis. It is perhaps time again for bankers to learn convex analysis.
The talk will be divided into two parts. In the first part we layout a discrete model for financial markets. We explain the concept of arbitrage and the no arbitrage principle. This is followed by the important fundamental theorem of asset pricing in which the no arbitrage condition is characterized by the existence of martingale (risk neutral) measures. The proof of this gives us a first taste of the importance of convex analysis tools. We then discuss how to use utility functions and risk measures to characterize the preference of market agents. The second part of the talk focuses on the issue of pricing financial derivatives. We use simple models to illustrate the idea of the prevailing Black Scholes replicating portfolio pricing method and related CoxRoss riskneutral pricing method for financial derivatives. Then, we show that the replicating portfolio pricing method is a special case of portfolio optimization and the risk neutral measure is a natural byproduct of solving the dual problem. Taking the convex analysis perspective of these methods h
 Download: Presentation (1.3 MB)
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Peter Forrester, Department of Mathematics and Statistics, The University of Melbourne
 Title: Selberg integrals and random matrix theory
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 24^{th} Feb 2011
 Abstract:
"In this talk I'll exhibit the interplay between
Selberg integrals (interpreted broadly) and random matrix theory.
Here an important role is played by the basic matrix operations of
a random corank 1 projection (this reduces the number of
nonzero eigenvalues by one) and bordering (this increases the
number of eigenvalues by one)."
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Various Members, CARMA, The University of Newcastle
 Title: 2011 Vacation Scholar Presentations
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 1:00 pm, Thu, 24^{th} Feb 2011
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Brian Corrie, The IRMACS Centre, Simon Fraser University
 Title: Collaboration in the Computational Sciences: Why, Where, What, and How
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} Feb 2011
 Abstract:
Research, as an activity, is fundamentally collaborative in nature. Driven by the massive amounts of data that are produced by computational simulations and high resolution scientific sensors, datadriven collaboration is of particular importance in the computational sciences. In this talk, I will discuss our experiences in designing, deploying, and operating an Canada wide advanced collaboration infrastructure in the support of the computational sciences. In particular, I will focus on the importance of data in such collaborations and discuss how current collaboration tools are sorely lacking in their support of datacentric
collaboration.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Roberto Cominetti, Departamento de Ingenieria Industrial, Universidad de Chile
 Title: Network Congestion Control with Markovian Multipath Routing
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 4:00 pm, Tue, 8^{th} Feb 2011
 Abstract:
We describe an integrated model for TCP/IP protocols with multipath routing. The model combines a Network Utility Maximization for rate control, with a Markovian Traffic Equilibrium for routing. This yields a crosslayer design in which sources minimize the expected cost of sending flows, while routers distribute the incoming flow among the outgoing links according to a discrete choice model. We prove the existence of a unique equilibrium state, which is characterized as the solution of an unconstrained strictly convex program of low dimension. A distributed algorithm for solving this optimization problem is proposed, with a brief discussion of how it can be implemented by adapting current Internet protocols.
Talk in [PDF]
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Roberto Cominetti, Departamento de Ingenieria Industrial, Universidad de Chile
 Title: ShortTerm Revenue Management: Optimal Targeting of Customers for a LastMinute Offer
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Mon, 7^{th} Feb 2011
 Abstract:
We discuss a shortterm revenue optimization problem that involves the optimal
targeting of customers for a promotional sale in which a finite number of perishable
items are offered on a lastminute offer. The goal is to select the subset of customers
to whom the offer will be made available, maximizing the expected return.
Each client replies with a certain probability and reports a specific value that depends
on the customer type, so that the selected subset has to balance the risk of not selling
all the items with the risk of assigning an item to a low value customer.
Selecting all those clients with values above a certain optimal threshold may fail to achieve
the maximal revenue. However, using a linear programming relaxation, we prove that such
threshold strategies attain a constant factor of the optimal value. The achieved factor is
${1\over 2}$ when a single item is to be sold, and approaches 1 as the number of available
items grows to infinity. Furthermore, for the single item case, we propose an upper bound
based on an exponential size linear program that allows us to get a threshold strategy achieving
at least ${2\over 3}$ of the optimal revenue. Computational experiments with random instances
show a significantly better performance than the theoretical predictions.
Talk in [PDF]
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Warren Moors, Department of Mathematics, The University of Auckland
 Title: Fixed Points Theorems and their Applications
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 27^{th} Jan 2011
 Abstract:
In this talk I will give some classical fixed point theorems and present some of their applications. The talk will be of a "Chalk and Talk" style and will include some elegant classical proofs. The down side of this is that the listener will be expected to have some familiarity with metric spaces, convexity and hopefully Zorn's Lemma.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Stephen Glasby, Department of Mathematics, Central Washington University
 Title: Insights into rational numbers through computation and geometry
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Mon, 13^{th} Dec 2010
 Abstract:
Rational numbers can be represented in many different ways: as a fraction, as a M"obius function, as a 2x2 matrix, as a string of L's and R's, as a continued fraction, as a disc in the plane, or as a point in the lattice Z^2. Converting between the representations involves interesting questions about computation and geometry. The geometries that arise are hyperbolic, inversive, or projective.
 [Permanent event link]
 CARMA COLLOQUIUM
 Maths Honours Student Presentation
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Thu, 25^{th} Nov 2010
 Speaker: Mr Chris Banks, CARMA, The University of Newcastle
 Title: Locally primitive groups acting on regular trees
 Abstract for Locally primitive groups acting on regular trees:
Automorphism groups of locally finite trees form a significant class of examples of locally compact totally disconnected topological groups. In this talk I will discuss my honours research, which covered the various local properties of automorphism groups. I will provide methods of constructing such groups, in particular groups acting on regular trees, and discuss what conclusions we can make regarding the structure of these groups.
 Speaker: Mr James Mainey, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: TBA
 Speaker: Mr Chris Maitland, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Methods for packing complete graphs with cycles
 Abstract for Methods for packing complete graphs with cycles:
This talk will be an introduction to cycle decompositions of complete graphs in the context of Alspach's conjecture about the necessary and sufficient conditions for their existence. Several useful methods of construction based on algebra, graph products and modifying existing decompositions will be presented. The most up to date results on this problem will be mentioned and future directions of study may be suggested.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Alexander Weiss, IANS, University of Stuttgart
 Title: Numerical simulation for twophase flow in complex pourous media systems
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Wed, 24^{th} Nov 2010
 Abstract:
In this talk we consider twophase flow models in porous media as they occur in several applications like oil production, pollute transport or CO2storage. After a general introduction, we focus on an enhanced model where the capillary pressure is ratedependent. We discuss the consequences of this term for heterogeneous materials with and without entry pressure. In the case of entry pressures the problem can be reformulation as inequality constraint at the material interface. Suitable discretization schemes and solution algorithms are proposed and used in various numerical simulations.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
 Title: Random subgroups of Thompson's group F
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 18^{th} Nov 2010
 Abstract:
What is a {\em random subgroup} of a group, and who cares? In a (nonabelian) group based cryptosystem, two parties (Alice and Bob) each choose a subgroup of some platform group "at random"  each picks $k$ elements "at random" and takes the subgroup generated by their chosen elements.
But for some platform groups (like the braid groups, which were chosen first, being so complicated and difficult) a "random subgroup" is not so random after all. It turned out, pick $k$ elements of a braid group, and they will generate (almost always) a {\em free group} with your $k$ elements as the free basis. And if Alice and Bob are just playing with free groups, it makes their secrets easy to attack.
Richard Thompson's group $F$ is an infinite, torsion free group, with many weird and cool properties, but the one I liked for this project is that it has {\em no} free subgroups (of rank $>1$) at all, so a random subgroup of $F$ could not be free  so what would it be?
This is joint work with Sean Cleary (CUNY), Andrew Rechnitzer (UBC) and Jeniffer Taback (Bowdoin).
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Eric Mortenson, School of Mathematics and Physics, The University of Queensland
 Title: Ramanujan, partitions, and mock theta functions
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 11^{th} Nov 2010
 Abstract:
We will give a brief overview and of the history of Ramanujan and give samplings of areas such as partitions, partition congruences, ranks, modular forms, and mock theta functions.
For example: A partition of a positive number $n$ is a nonincreasing sequence of positive integers whose sum is $n$. There are five partitions of the number four: 4, 3+1, 2+2, 2+1+1, 1,1,1,1. If we let $p(n)$ be the number of partitions of $n$, it turns out that $p(5n+4)\equiv \pmod{5}$. How does one explain this?
Once the basics and context have been introduced, we will discuss new results with respect to mock theta functions and show how they relate to old and recent results.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
 Title: Ramanujan's ArithmeticGeometric Mean Continued Fractions and Dynamics
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 4^{th} Nov 2010
 Abstract:
The continued fraction:
$${\cal R}_\eta(a,b) =\,\frac{{\bf \it a}}{\displaystyle
\eta+\frac{\bf \it b^2}{\displaystyle \eta
+\frac{4{\bf \it a}^2}{\displaystyle \eta+\frac{9 {\bf \it b}^2}{\displaystyle \eta+{}_{\ddots}}}}}$$
enjoys attractive algebraic properties such as a striking arithmeticgeometric mean relation and elegant links with ellipticfunction theory. The fraction presents a computational challenge, which we could not resist.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle
 Title: Maximal antichains on two levels of the Boolean lattice
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 28^{th} Oct 2010
 Abstract:
We are looking at families of finite sets, more specifically subsets of [n]={1,2,...,n}. In particular, we are interested in antichains, that means no member of the family is contained in another one. In this talk we focus on antichains containing only sets of two different cardinalities, say k and l, and study the question what the smallest size of a maximal antichain is (maximal in the sense that it is impossible to add any kset or lset without violating the antichain property). This can be nicely reformulated as a problem in extremal (hyper)graph theory, looking similar to the Turán problem on the maximum number of edges in a graph without a complete subgraphs on l vertices. We sketch the solution for the case (k,l)=(2,3), conjecture an optimal construction for the case (k,l)=(2,4) and present some asymptotic bounds for this case.
 [Permanent event link]
 CARMA COLLOQUIUM AND SIGMAOPT SEMINAR
 Speaker: Angelos Tsoukalas , School of Mathematical and Geospatial Sciences, RMIT University
 Title: Using Cutting Planes in the Feasibility Pump
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: RMIT
 Time and Date: 3:30 pm, Wed, 27^{th} Oct 2010
 Abstract:
We discuss the feasibility pump heuristic and we interpret it as a multistart, global optimization algorithm that utilizes a fast local minimizer. The function that is minimized has many local minima, some of which correspond to feasible integral solutions. This interpretation suggests alternative ways of incorporating restarts one of which is the use of cutting planes to eliminate local optima that do not correspond to feasible integral solutions. Numerical experiments show encouraging results on standard test libraries.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Fuji Zhang, School of Mathematics, Xiamen University
 Title: The Matching Polynomial and the Location of its Roots
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 21^{st} Oct 2010
 Abstract:
The Matching Polynomial is a topic in the area of mathematics, statistical physics (dimermolomer problem) and chemistry (topological resonant energy). In this talk we will discuss the computation of matching polynomial and location of its roots. We show that the roots of matching generating polynomials of graphs are dense in (−∞, 0] and the roots of matching polynomials of graphs dense in (−∞,+∞) which answer a problem of Brown et. al. (see Journal of Algebraic Combinatorics, 19, 273–282, 2004). Some similar result in characteristic polynomial, independent polynomial and chromatic polynomial are also presented. [Also speaking: Prof Weigen Yan]
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Prof Stephen Watt, University of Western Ontario
 Title: The Mathematics of Mathematical Handwriting Recognition
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 11:00 am, Fri, 15^{th} Oct 2010
 Abstract:
Accurate computer recognition of handwritten mathematics offers to provide a natural interface for mathematical computing, document creation and collaboration. Mathematical handwriting, however, provides a number of challenges beyond what is required for the recognition of handwritten natural languages. For example, it is usual to use symbols from a range of different alphabets and there are many similarlooking symbols. Many writers are unfamiliar with the symbols they must use and therefore write them incorrectly. Mathematical notation is twodimensional and size and placement information is important. Additionally, there is no fixed vocabulary of mathematical "words" that can be used to disambiguate symbol sequences. On the other hand there are some simplifications. For example, symbols do tend to be wellsegmented. With these charactersitics, new methods of character recognition are important for accurate handwritten mathematics input.
 [Permanent event link]
 CARMA COLLOQUIUM
 Speaker: Armin Staub, Tulane University
 Title: On infinite logconcavity
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 14^{th} Oct 2010
 Abstract:
The logconcavity of a sequence is a much studied concept in combinatorics with surprising links to many other mathematical fields. In this talk we discuss the stronger but much less studied notion of mfold logconcavity which has recently recieved some attention after Boros and Moll conjectured that a "remarkable" sequence encountered in the integration of an inverse cubic is infinitely logconcave. In particular, we report on a recent result of Branden which implies infinite logconcavity of the binomial coefficients and other new developments. Examples and conjectures are promised. A PDF of the talk is available here.
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 CARMA COLLOQUIUM
 Speaker: Prof Martin Groetschel, Institute of Mathematics, Technical University of Berlin
 Title: LP and MIP solving in theory and practice
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 2:30 pm, Mon, 11^{th} Oct 2010
 Abstract:
There are many algorithms with which linear programs (LPs)
can be solved (FourierMotzkin, simplex, barrier, ellipsoid,
subgradient, bundle, ...). I will provide a very brief review of these
methods and their advantages and disadvantages. An LP solver is the main
ingredient of every solution method.(branch&bound, cutting planes, column generation, ...) for (NP hard)
mixedinteger linear programs (MIPs). What combinations of which
techniques work well in practice? There is no general answer. I will
show, by means of many practical examples from my research group
(telecommunication, transport, traffic and logistics, energy, ...), how
large scale LPs and MIPs are successfully attacked today.
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 CARMA COLLOQUIUM
 Speaker: Eduardo Castillo, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Connections between geometrical and fixed point properties
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 7^{th} Oct 2010
 Abstract:
In the area of Metric Fixed Point Theory, one of the outstanding question was if the fixed point property implied reflexivity. This question was answered in the negative in 2008 by P.K.Lin, when he showed that certain renorm in the space of absolutely sumable sequences, had the fixed point property. In this talk we will show a general way to renorm certain spaces in order to have the fixed point property. We also give general properties for a given Banach space to enjoy the f.p.p. And we will also show equivalences of geometrical properties to certain fixed point properties.
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 CARMA COLLOQUIUM
 Speaker: Wayne Lawton, National University of Singapore
 Title: Spectral Envelopes of Integer Subsets
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 23^{rd} Sep 2010
 Abstract:
The design of signals with specified frequencies has applications in numerous fields including acoustics, antenna beamforming, digital filters, optics, radar, and time series analysis. It is often desirable to concentrate signal intensity in certain locations and design methods for this have been intensively studied and are well understood. However, these methods assume that the specified frequencies consist of an interval of integers. What happens when this assumption fails is almost a complete mystery that this talk will attempt to address.
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 CARMA COLLOQUIUM
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 16^{th} Sep 2010
 Please note that there is no CARMA Colloquium this week.
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 CARMA COLLOQUIUM
 Speaker: Prof John Giles, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: A Continuity Characterisation of Asplund Spaces
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 2^{nd} Sep 2010
 Abstract:
An Asplund space is a Banach space which possesses desirable differentiability properties enjoyed by Euclidean spaces. Many characterisations of such spaces fall into two classes: (i) those where an equivalent norm possesses a particular general property, (ii) those where every equivalent norm possesses a particular property at some points of the space. For example: (i) X is an Asplund space if there exists an equivalent norm Frechet differentiable on the unit sphere of the space, (ii) X is an Asplund space if every equivalent norm is Frechet differentiable at some point of its unit sphere. In 1993 (FP) showed that (i) X is an Asplund space if there exists an equivalent norm strongly subdifferentiable on the unit sphere of the space and in 1995 (GMZ) showed that (ii) X separable is an Asplund space if every equivalent norm is strongly subdifferentiable at a nonzero point of X. Problem: Is this last result true for nonseparable spaces? In 1994 (CP) showed (i) X is an Asplund space if there exists an equivalent norm with subdifferential mapping Hausdorff weak upper semicontinuous on its unit sphere. We show: (ii) X is an Asplund space if every continuous gauge on X has a point where its subdifferential mapping is Hausdorff weak upper semicontinuous with weakly compact image which is some way towards solving the problem.
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 CARMA COLLOQUIUM
 Speaker: Marc Lassonde, Laboratoire de Mathématiques Informatique et Applications (LAMIA), Université des Antilles et de la Guyane
 Title: Asplund spaces, Stegall variational principle and the RNP
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Mon, 23^{rd} Aug 2010
 Abstract:
Given a pair of Banach spaces X and Y such that one is the dual of the other, we study the relationships between generic Fr´echet differentiability of convex continuous functions on Y (Asplund property), generic existence of linear perturbations for lower semicontinuous functions on X to have a strong minimum (Stegall variational principle), and dentability of bounded subsets of X (RadonNikod´ym Property).
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 CARMA COLLOQUIUM
 Speaker: Julian Revalski, Laboratoire de Mathématiques Informatique et Applications (LAMIA), Université des Antilles et de la Guyane
 Title: Regularization procedures for monotone operators
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 11:00 am, Fri, 20^{th} Aug 2010
 Abstract:
In this talk we will focus our attention on certain regularization techniques related to two operations involving monotone operators: pointwise sums of maximal monotone operators and precompositions of such operators with linear continuous mappings. These techniques, whose underlying idea is to obtain a bigger operator as a result, lead to two concepts of generalized operationsextended and variational sums of maximal monotone operators and, the corresponding to them, extended and variational compositions of monotone mappings with linear continuous operators. We will revue some of the basic results concerning these generalized concepts, as well as will present some recent important advances.
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 CARMA COLLOQUIUM
 Speaker: Steve Mohr, School of Engineering, The University of Newcastle
 Title: Projection of world fossil fuel production with supply and demand interactions
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 19^{th} Aug 2010
 Abstract:
Historically, fossil fuels have been vital for our global energy needs. However climate change is prompting renewed interest in the role of fossil fuel production for our energy needs. In order to appropriately plan for our future energy needs, a new detailed model of fossil fuel supply is required. The modelling applied an algorithmbased approach to predict both supply and demand for coal, gas, oil and total fossil fuel resources. Total fossil fuel demand was calculated globally, based on world population and per capita demand; while production was calculated on a countrybycountry basis and summed to obtain global production. Notably, production over the lifetime of a fuel source was not assumed to be symmetrical about a peak value like that depicted by a Hubbert curve. Separate production models were developed for mining (coal and unconventional oil) and field (gas and conventional oil) operations, which reflected the basic differences in extraction and processing techniques. Both of these models included a number of parameters that were fitted to historical production data, including: (1) coal for New South Wales, Australia; (2) gas from the North Sea, UK; and (3) oil from the North Sea, UK, and individual state data from the USA.
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 CARMA COLLOQUIUM
 Speaker: Dr Jeff Hogan, CARMA, The University of Newcastle
 Title: Prolate spheroidal wavefunctions and the "lucky accident"
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 5^{th} Aug 2010
 Abstract:
The classical prolate spheroidal wavefunctions (prolates) arise when solving the Helmholtz equation by separation of variables in prolate spheroidal coordinates. They interpolate between Legendre polynomials and Hermite functions. In a beautiful series of papers published in the Bell Labs Technical Journal in the 1960's, they were rediscovered by Landau, Slepian and Pollak in connection with the spectral concentration problem. After years spent out of the limelight while wavelets drew the focus of mathematicians, physicists and electrical engineers, the popularity of the prolates has recently surged through their appearance in certain communication technologies. In this talk we discuss the remarkable properties of these functions, the ``lucky accident'' which enables their efficient computation, and give details of their role in the localised sampling of bandlimited signals.
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 CARMA COLLOQUIUM
 Speaker: Dr Bishnu Lamichhane, CARMA, The University of Newcastle
 Title: HuWashizu Formulation
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:00 pm, Thu, 29^{th} Jul 2010
 Abstract:
The HuWashizu formulation in elasticity is the mother of many different finite element methods in engineering computation. We present some modified HuWashizu formulations and their performance in removing locking effect in the nearly incompressible elasticity. The stabilisation of the standard HuWashizu formulation is used to obtain the stabilised nodal strain formulation or nodebased uniform strain elements. However, we show that standard or stabilised nodal strain formulation should be modified to have a uniformly convergent finite element approximation in the nearly incompressible case.
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 CARMA COLLOQUIUM
 Speaker: Dr Maicon Alvez, Universidade Federal de Santa Catarina
 Title: Some results on maximal monotone operators in nonreflexive Banach spaces
 Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 15^{th} Jul 2010
 Abstract:
In this talk we will present some results recently obtained in collaboration with B.F.Svaiter on maximal monotone operators in nonreflexive Banach spaces. The focus will be on the use of concept of convex representation of a maximal monotone operator for obtaining results on these operators of type: surjectivity of perturbations by duality mappings, uniqueness of the extension to the bidual, BrondstedRockafellar property, etc.
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 CARMA COLLOQUIUM AND SIGMAOPT SEMINAR
 Speaker: Conjoint Prof Steve Wright, Computer Sciences Department and Wisconsin Institute for Discovery, University of WisconsinMadison
 Title: More Tools and Applications of Sparse Optimization
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 4:00 pm, Thu, 24^{th} Jun 2010
 Abstract:
Machine learning problems are a particularly rich source of applications for sparse optimization, giving rise to a number of formulations that require specialized solvers and structured, approximate solutions. As case studies, we discuss two such applications  sparse SVM classification and sparse logistic regression  and present algorithms that are assembled from different components, including stochastic gradient methods, random approximate matrix factorizations, block coordinate descent, and projected Newton methods. We also describe a third (distantly related) application to selection of captive breeding populations for endangered species using binary quadratic programming, a project started during a visit to Newcastle in June 2009.
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 CARMA COLLOQUIUM
 Speaker: Prof David Gao, Alexander Rubinov Professor of Mathematics, The University of Ballarat
 Title: Optimization and Control of Complex Systems: Canonical Duality Approach
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: RMIT
 Time and Date: 4:00 pm, Thu, 17^{th} Jun 2010
 Abstract:
Nonconvex/nonsmooth phenomena appear naturally in many complex systems. In static systems and global optimization problems, the nonconvexity usually leads to multisolutions in the related governing equations. Each of these solutions represents certain possible state of the system. How to identify the global and local stability and extremality of these critical solutions is a challenge task in nonconvex analysis and global optimization. The classical Lagrangiantype methods and the modern FenchelMoreauRockafellar duality theories usually produce the wellknown duality gap. It turns out that many nonconvex problems in global optimization and computational science are considered to be NPhard. In nonlinear dynamics, the socalled chaotic behavior is mainly due to nonconvexity of the objective functions. In nonlinear variational analysis and partial differential equations, the existence of nonsmooth solutions has been considered as an outstanding open problem. In this talk, the speaker will present a potentially useful canonical duality theory for solving a class of optimization and control problems in complex systems. Starting from a very simple cubic nonlinear equation, the speaker will show that the optimal solutions for nonconvex systems are usually nonsmooth and cannot be captured by traditional local analysis and Newtontype methods. Based on the fundamental definitions of the objectivity and isotropy in continuum physics, the canonical duality theory is naturally developed, and can be used for solving a large class of nonconvex/nonsmooth/discrete problems in complex systems. The results illustrate the important fact that smooth analytic or numerical solutions of a nonlinear mixed boundaryvalue problem might not be minimizers of the associated variational problem. From a dual perspective, the convergence (or nonconvergence) of the FDM is explained and numerical examples are provided. This talk should bring some new insights into nonconvex analysis, global optimization, and computational methods.
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 CARMA COLLOQUIUM
 Speaker: Prof Michael Barnsley, Mathematical Sciences Institute, Australian National University
 Title: Theory and Applications of Fractal Transformations
 Location: Room VG10, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} Jun 2010
 Abstract:
This talk will introduce fractal transformations and some of their remarkable properties. I will explain the mathematics that sustains them and how to construct them in simple cases. In particular I hope to demonstrate a very recent result, showing how they can be applied to generate convenient mutuallysingular measures that enable the storage of multiple images within a single image. The talk will include some beautiful computer graphics.
 Prof Michael Barnsley, the author of "Fractals Everywhere", will be talking in CARMA's Thursday Colloquium series on iterated function systems.
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