Priority Research Centre for Computer-AssistedResearch Mathematics and its Applications
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### CARMA-Sponsored Seminar Series: Colloquia, Seminars and More.

[Note: events are listed by descending date.]
 CARMA COLLOQUIUM Speaker: A/Prof Duangkamon Baowan, Department of Mathematics, Mahidol University Title: Calculus of variations and the bending of carbon nanostructures Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Wed, 24th Apr 2019 Abstract: Calculus of variations is utilized to minimize the elastic energy arising from the curvature squared while maximizing the van der Waals energy. Firstly, the shape of folded graphene sheets is investigated, and an arbitrary constant arising by integrating the Euler–Lagrange equation is determined. In this study, the structure is assumed to have a translational symmetry along the fold, so that the problem may be reduced to a two dimensional problem with reflective symmetry across the fold. Secondly, both variational calculus technique and least squared minimization procedure are employed to determine the joining structure involved a C60 fullerene and a carbon nanotube, namely a nanobud. We find that these two methods are in reasonable overall agreement. However, there is no experimental or simulation data to determine which procedure gives the more realistic results. [Permanent event link] CARMA COLLOQUIUM Speaker: Dr Scott Lindstrom, Hong Kong Polytechnic University Title: Optimisation models for data science and machine learning Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 18th Apr 2019 Abstract: We discuss various optimisation-based approaches to machine learning. Tasks include regression, clustering, and classification. We discuss frequently used terms like 'unsupervised learning,' 'penalty methods,' and 'dual problem.' We motivate our discussion with simple examples and visualisations. [Permanent event link] CARMA COLLOQUIUM Speaker: Professor Claudio Altafini, Linkoping University Title: Decision-making in interconnected multiagent networks: roles of frustration and social commitment Location: Room LSTH, Life Sciences Lecture Theatre (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 11th Apr 2019 Abstract: The models of collective decision-making considered in this presentation are nonlinear interconnected systems with saturating interactions, similar to Hopfield newtorks. These systems encode the possible outcomes of a decision process into different steady states of the dynamics. When the model is cooperative, i.e., when the underlying adjacency graph is Metzler, then the system is characterized by the presence of two main attractors, one positive and the other negative, representing two choices of agreement among the agents, associated to the Perron-Frobenius eigenvector of the system. Such equilibria are achieved when there is a sufficiently high 'social commitment' among the agent (here interpreted as a bifurcation parameter). When instead cooperation and antagonism coexist, the resulting signed graph is in general not structurally balanced, meaning that Perron-Frobenius theorem does not apply directly. It is shown that the decision-making process is affected by the distance to structural balance, in the sense that the higher the frustration of the graph, the higher the commitment strength at which the system bifurcates. In both cases, it is possible to give conditions on the commitment strength beyond which other equilibria start to appear. These extra bifurcations are related to the algebraic connectivity of the graph. [Permanent event link] CARMA COLLOQUIUM Speaker: A/Prof Alessandro Toffoli, The University of Melbourne Title: Sailing through a polar cyclone to witnes the fierceness of the Southern Ocean: there and back again Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle Time and Date: 2:00 pm, Thu, 11th Apr 2019 Abstract: Sea ice acts as a refrigerator for the world. Its bright surface reflects solar heat, and the salt it expels during the freezing process drives cold water towards the equator. As a result, sea ice plays a crucial role in our climate system. Antarctic sea-ice extent has shown a large degree of regional variability, in stark contrast with the steady decreasing trend found in the Arctic. This variability is within the ranges of natural fluctuations, and may be ascribed to the high incidence of weather extremes, like intense cyclones, that give rise to large waves, significant wind drag, and ice deformation. The role exerted by waves on sea ice is still particular enigmatic and it has attracted a lot of attention over the past years. Starting from theoretical knowledge, new understanding based on experimental models and computational fluid dynamics is presented. But exploration of waves-in-ice cannot be exhausted without being on the field. And this is why I found myself in the middle of the Southern Ocean during a category five polar cyclone to measure waves… This talk will take place at 2pm, not the standard time. [Permanent event link] CARMA COLLOQUIUM Speaker: Professor Yann Bugeaud, Mathématiques , Université de Strasbourg Title: On the decimal expansion of $\log (2019/2018)$ and $e$ Location: Room LSTH, Life Sciences Lecture Theatre (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 4th Apr 2019 Abstract: It is commonly expected that $e$, $\log 2$, $\sqrt{2}$, among other « classical » numbers, behave, in many respects, like almost all real numbers. For instance, their decimal expansion should contain every finite block of digits from $\{0, \ldots , 9\}$. We are very far away from establishing such a strong assertion. However, there has been some small recent progress in that direction. Let $\xi$ be an irrational real number. Its irrationality exponent, denoted by $\mu (\xi)$, is the supremum of the real numbers $\mu$ for which there are infinitely many integer pairs $(p, q)$ such that $|\xi - \frac{p}{q}| < q^{-\mu}$. It measures the quality of approximation to $\xi$ by rationals. We always have $\mu (\xi) \ge 2$, with equality for almost all real numbers and for irrational algebraic numbers (by Roth's theorem). We prove that, if the irrationality exponent of $\xi$ is equal to $2$ or slightly greater than $2$, then the decimal expansion of $\xi$ cannot be too simple', in a suitable sense. Our result applies, among other classical numbers, to badly approximable numbers, non-zero rational powers of ${{\rm e}}$, and $\log (1 + \frac{1}{a})$, provided that the integer $a$ is sufficiently large. It establishes an unexpected connection between the irrationality exponent of a real number and its decimal expansion. Note that this talk is not in the standard room. It will be in the Life Sciences Lecture Theatre (LSTH). [Permanent event link] CARMA COLLOQUIUM Speaker: Professor Thomas Nann, School of Mathematical and Physical Sciences, The University of Newcastle Title: Math meets materials: the density-functional theory (DFT) Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 21st Mar 2019 Abstract: Imagine a world, where physical and chemical laboratories are unnecessary, because all experiments can be simulated accurately on a computer. In principle this is possible, solving the quantum mechanical Schrödinger equation. Unfortunately, this is far from trivial and practically impossible for large and complex materials and reactions. In 1998, Walter Kohn and John A Pople won the Nobel Prize in Chemistry for developing the density-functional theory (DFT). DFT allows to find solutions for the Schrödinger equation much more efficiently than ab-initio and similar approaches, thus enabling the computation of materials properties in an unprecedented way. In this seminar, I will introduce quantum mechanical principles and the basic idea of the DFT. Then, I will present an example of the computational elucidation of a reaction mechanism in materials science. [Permanent event link] CARMA COLLOQUIUM Speaker: A/Prof. Michael Coons, CARMA, The University of Newcastle Title: Mahler's methods: theorems, speculations and variations Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 14th Mar 2019 Abstract: Mahler's method in number theory is an area wherein one answers questions surrounding the transcendence and algebraic independence of both power series $F(z)$, which satisfy the functional equation $$a_0(z)F(z)+a_1(z)F(z^k)+\cdots+a_d(z)F(z^{k^d})=0$$ for some integers $k\geqslant 2$ and $d\geqslant 1$ and polynomials $a_0(z),\ldots,a_d(z)$, and their special values $F(\alpha)$, typically at algebraic numbers $\alpha$. The most important examples of Mahler functions arise from important sequences in theoretical computer science and dynamical systems, and many are related to digital properties of sets of numbers. For example, the generating function $T(z)$ of the Thue-Morse sequence, which is known to be the fixed point of a uniform morphism in computer science or equivalently a constant-length substitution system in dynamics, is a Mahler function. In 1930, Mahler proved that the numbers $T(\alpha)$ are transcendental for all non-zero algebraic numbers $\alpha$ in the complex open unit disc. With digital computers and computation so prevalent in our society, such results seem almost second nature these days and thinking about them is very natural. But what is one really trying to communicate by proving that functions or numbers such as those considered in Mahler's method? In this talk, highlighting work from the very beginning of Mahler's career, we speculate---and provide some variations---on what Mahler was really trying to understand. This talk will combine modern and historical methods and will be accessible to students. [Permanent event link] CARMA COLLOQUIUM Speaker: Prof Jeffrey Lagarias, University of Michigan Title: Packing Space with Regular Tetrahedra Location: Room SR202, SR Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Tue, 5th Mar 2019 Abstract: The problem of packing space with regular tetrahedra has a 2000 year history. This talk surveys the history of work on the problem. It includes work by mathematicians, computer scientists, physicists, chemists, and materials scientists. Much progress has been made on it in recent years, yet there remain many unsolved problems. This talk will be accessible to a very wide audience. [Permanent event link] CARMA COLLOQUIUM Speaker: Prof. Joseph Rosenblatt, Department of Mathematical Sciences, Indiana University-Purdue 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, 17th 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. [Permanent event link] 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, 10th 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Prof Brigitte Forster-Heinlein, 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, 31st Oct 2017 Abstract: We consider variations on the commutative diagram consisting of the Fourier transform, the Sampling Theorem and the Paley-Wiener Theorem. We start from a generalization of the Paley-Wiener theorem and consider entire functions with specific growth properties along half-lines. 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 Paley-Wiener 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Peter Massopust, Technical University of Munich Title: B-Splines and Beyond Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 12th Oct 2017 Abstract: Schoenberg’s polynomial cardinal B-splines of order $n$ provide a family of compactly supported $C^{n-2}$-functions. We present several generalizations of these B-splines, discuss their properties, and relate them to fractional difference and differentiation operators. Potential applications are mentioned. [Permanent event link] 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, 10th 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. [Permanent event link] 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, 2nd Aug 2017 Abstract: I will discuss how to relate regular origami tilings to vertex models in statistical mechanics. The Miura-ori origami pattern has found many uses in engineering as an auxetic metamaterial. I analyze the effect of crease assignment defects on the long-range order properties of the Miura-ori 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 long-range 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. [Permanent event link] 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, 20th 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 area-minimising. 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 infinite-dimensional 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. [Permanent event link] 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, 4th 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 non-trivial 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 L-systems, a family of classes of languages originally developed to model growth of algae, and show that the co-word 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 L-system. [Permanent event link] 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, 28th 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 small-scale and large-scale 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. [Permanent event link] 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, 9th 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. [Permanent event link] 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, 7th Mar 2017 Abstract: There is to date no overarching classification theorem for C*-algebras, which means the theory of C*-algebras is an example-driven 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Michael Bennett, University of British Columbia Title: Erdos-Selfridge and Supersingularity Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Tue, 28th 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. [Permanent event link] 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, 2nd 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. [Permanent event link] 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, 19th Oct 2016 Abstract: Many governments and international finance organisations use a carbon price in cost-benefit 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 high-level, 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. [Permanent event link] 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, 12th 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 JN-25, 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 JN-25 to be broken - probably the best-kept secret of the entire Pacific War: multiples of three! Good maths, but not highly technical! [Permanent event link] 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, 5th 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. [Permanent event link] 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, 10th 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, two-stage 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 post-decisional 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. [Permanent event link] 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, 3rd 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 square-particles that cannot overlap. This problem of "hard-squares" 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 golden-mean 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 hard-squares and related problems. This is work together with Yao-ban Chan. [Permanent event link] CARMA COLLOQUIUM Speaker: Michael Baake, Bielefeld Title: Dynamical Systems of number-theoretic 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, 23rd 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 square-free 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Florian Luca, University of the Witwatersrand Title: Diophantine m-tuples Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 28th Jan 2016 Abstract: A diophantine m-tuple is a set of m-positive 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Assen Dontchev, University of Michigan Title: The four theorems by Lawrence M. Graves Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 21st Jan 2016 Abstract: This talk is devoted to three basic forms of the inverse function theorem. The classical inverse function theorem identify a smooth single-valued localization of the inverse on the condition of nonsingularity of the Jacobian. Download: Presentation (231 KB) [Permanent event link] CARMA COLLOQUIUM Speaker: Prof Frank Garvan, University of Florida Title: Transformation Properties for Dyson's Rank Fun Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Wed, 16th Dec 2015 Abstract: At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. We extend the work of Bringmann and Ono, and Ahlgren and Treneer on answering this question. [Permanent event link] 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, 22nd 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Karl Dilcher, Mathematics and Statistics, Dalhousie University Title: Zeros and irreducibility of gcd-polynomials Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 15th Oct 2015 Abstract: We study the family of self-inversive 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 self-inversive polynomials and of their "duals" obtained from the discrete Fourier transforms of the coefficients sequence. (Joint work with Sinai Robins). [Permanent event link] 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, 10th 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. [Permanent event link] 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, 9th 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 pre-processing 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 widely-used Period Event Scheduling Problem (PESP). [Permanent event link] 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, 11th 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 cross-frequency 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 time-frequency 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 time-frequency localized signals, so-called 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. [Permanent event link] CARMA COLLOQUIUM Speaker: David Pask, University of Wollongong Title: Textile systems, Wang tiles, 2-coloured graphs and 2-graphs Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 21st May 2015 Abstract: In this colloquium-style presentation I will describe these combinatorial objects and how they relate to each other. Time permitting, I will also show how they can be used in other areas of Mathematics. Joint work with Sooran Kang and Samuel Webster. [Permanent event link] 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, 14th 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: I prefer Pi, a talk for 3.14.15 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 12th Mar 2015 Abstract: In celebration of both a special "big" pi Day (3/14/15) and the 2015 centennial of the Mathematical Association of America, we review the illustrious history of the constant $\pi$ in the pages of the American Mathematical Monthly. [Permanent event link] 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, 11th 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. [Permanent event link] 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, 5th 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 tree-like structures inside the Diophantine set of interest. In this talk I will discuss how one broad method of tree-like 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 so-called 'Cantor-winning' 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. [Permanent event link] CARMA COLLOQUIUM Speaker: William McLean, University of NSW Title: Error bounds for time stepping of fractional diffusion equations with non-smooth initial data Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 18th 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Markus Hegland, Mathematical Sciences Institute, Australian National University Title: Tensor trains to deal with the curse of dimensionality? -- definition, examples and algorithms Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 6th Nov 2014 Abstract: Tensor trains are a new class of functions which are thought to have some potential to deal with high-dimensional problems. While connected with algebraic geometry the main concepts used are rank-k matrix factorisations. In this talk I will review some basic properties of tensor trains. In particular I will consider algorithms for the solution of linear systems Ax=0. This talk is related to research in progress with Jochen Garcke (Uni Bonn and Fraunhofer Institute) on the solution of the chemical master equation. This talk assumes a basic background in matrix algebra. No background in algebraic geometry is required. [Permanent event link] 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, 3rd Nov 2014 - Mon, 3rd Nov 2014 [Permanent event link] 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, 9th 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 wave-ice interaction. [Permanent event link] 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, 2nd 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 algebraic-geometric concepts and modern convex programming (semi-definite programming). In this talk, we will discuss some recent progress of the polynomial (semi-algebraic) 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 semi-algebraic structure helps us to analyze some important and classical algorithms in optimization such as alternating projection algorithm, proximal point algorithm and Douglas-Rachford 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, 29th Sep 2014 - Mon, 29th Sep 2014 Abstract: Third lecture: metric properties. [Permanent event link] CARMA COLLOQUIUM Speaker: A/Prof. Michael Coons, CARMA, The University of Newcastle Title: Variations on a theme of Mahler Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 25th Sep 2014 Abstract: I will survey some recent and not-so-recent results surrounding the areas of Diophantine approximation and Mahler's method related to variations of the Chomsky-Schützenberger hierarchy. [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, 22nd Sep 2014 - Mon, 22nd Sep 2014 [Permanent event link] CARMA COLLOQUIUM Speaker: ARC Laureate Fellow 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, 11th 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 complex-valued 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 integer-valued 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 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, 8th Sep 2014 - Mon, 8th Sep 2014 Abstract: This is the first in a series of lectures on this fascinating group. [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, 14th Aug 2014 Abstract: We present a PSPACE-algorithm 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 real-world constraints Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Wed, 23rd Jul 2014 Abstract: A vast amount of natural processes can be modelled by partial differential equations involving diffusion operators. The Navier-Stokes 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 non-linear 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 non-physical 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, 5th 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 Euler-Lagrange equation. We show the link between the Euler-Lagrange 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, 29th 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, 1885-1977, 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 multi-core 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, 21st 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, 1885-1977, 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 multi-core 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, 16th 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: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Seeing things by walking on real numbers Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Wed, 9th Apr 2014 Abstract: I will describe the research I have been doing with Fran Aragon and others, using graphical methods to study the properties of real numbers. There will be very few formulas and more pictures and movies. [Permanent event link] CARMA COLLOQUIUM Speaker: Dr Judy-anne 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, 27th Feb 2014 Abstract: Brad Pitt's zombie-attack movie "World War Z" may not seem like a natural jumping-off 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 possibility-space. The same mathematical models can let us playfully explore how an outbreak of zombie-ism 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, 12th Feb 2014 Abstract: This talk will give an introduction to the Kelper-Coulomb 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: ARC Laureate Fellow George Willis, CARMA, The University of Newcastle Title: Visualising Numbers Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Wed, 11th Dec 2013 Abstract: I will review the creation and development of the concept of number and the role of visualisation in that development. The relationship between innate human capabilities on the one hand and mathematical research and education on the other will be discussed. Download: Talk slides (100 KB) [Permanent event link] CARMA COLLOQUIUM Speaker: ARC Laureate Fellow 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, 28th 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, 14th 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, 31st 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 non-trivially knotted with certain topologies preferred over others. The aim of our work is to determine the "natural" distribution of different knot-types 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 - self-avoiding 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 knot-types is universal. Our data shows that a long closed curve is about 28 times more likely to be a trefoil than a figure-eight, 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, 12th 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, 29th 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 NP-hard. [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, 1st Nov 2012 Abstract: I will give an extended version of my talk at the AustMS meeting about some ongoing work with Pierre-Emmanuel 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 well-understood. 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 non-discrete 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 likelihood-free 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, 24th 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 likelihood-free 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 rejection-based method and scale to high-dimensional parameter spaces that have proven difficult for the current rejection-based ABC methods. To illustrate its utility we apply ABCDE to several well-established simulation-based models of memory and decision-making 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, 11th 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, 13th 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 high-tech businessman. I will also offer advice that can of course be ignored. [Permanent event link] CARMA COLLOQUIUM Speaker: Prof A. Bass Bagayogo, Université de Saint-Boniface 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, 23rd 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 Navier-Stokes 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: A/Prof. 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, 9th 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 Thue-Morse 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, 26th 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, 5th 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: Dr Jean Lasserre, LAAS-CNRS, Université de Toulouse Title: Moments, Positive Polynomials and Semidefinite Programming Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 5th Apr 2012 [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, 3rd 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, 9th 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 claw-free graphs and techniques that allow to reduce the problem to cubic graphs. The approach will be illustrated on a recently introduced closure concept for Hamilton-connectedness in claw-free graphs and, as an application, an asymptotically sharp Ore-type degree condition for Hamilton-connectedness in claw-free graphs will be obtained. [Permanent event link] CARMA COLLOQUIUM Speaker: Dr Ville Merila, CARMA, The University of Newcastle Title: A glimpse at Diophantine approximation of q-series Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 17th Nov 2011 Abstract: In this talk I attempt to explain a general approach in proving irrationality and linear independence results for q-hypergeometric series. An explicit Pade construction is introduced with some (quantitative) arithmetic implications for well-known q-mathematical constants. [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, 3rd 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, 20th Oct 2011 Abstract: Mean periodic functions of a single real variable were an innovation of the mid-20th 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 Compactly-Generated to Well-Generated Triangulated Categories Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 13th 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 Multi-Plan Method for Radiotherapy Treatment Design via Finite Representation of the Non-Dominated Set of a Multi-Objective Linear Programme Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Fri, 30th Sep 2011 Abstract: The choice of a plan for radiotherapy treatment for an individual cancer patient requires the careful trade-off 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 multi-objective linear programme (MOLP). In this talk we present a method to compute a finite set of non-dominated points that can be proven to uniformly cover the complete non-dominated 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 trial-and-error 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, 15th 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 well-known 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 pattern-avoiding permutations Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 18th Aug 2011 Abstract: Given a mixed-up sequence of distinct numbers, say 4 2 1 5 7 3 6, can you pass them through an infinite stack (first-in-last-out) 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, 4th 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: Hand-to-Hand Combat with Thousand-Digit Integrals Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 12:00 pm, Fri, 22nd 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 well-known 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, 21st 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 Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness 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 well-recognized 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, 14th 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 $\zeta(2 s-1)$, 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: High-dimensional Numerical Integration Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 16th Jun 2011 Abstract: High-dimensional 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 equal-weight quadrature rules called quasi-Monte Carlo. These rules are defined over the unit cube $[0,1]^s$ with carefully chosen quadrature points. The quadrature points can be obtained using number-theoretic 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 one-dimensional case, the discrepancy coincides with the Kolmogorov-Smirnov 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: Dr Thanh Tran, School of Mathematics and Statistics, University of NSW Title: Numerical Methods for the Landau-Lifshitz-Gilbert Equation Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 9th Jun 2011 Abstract: The Landau-Lifshitz-Gilbert equation (LLGE) comes from a model for the dynamics of the magnetization of a ferromagnetic material. In this talk we will first describe existing finite element methods for numerical solution of the deterministic and stochastic LLGEs. We will then present another finite element solution to the stochastic LLGE. This is a work in progress jointly with B. Goldys and K-N Le. Download: Seminar slides (511 KB) [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, 26th 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, 19th May 2011 Abstract: In the late seventies, Bill Thurston defined a semi-norm on the homology of a 3-dimensional 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, 5th 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 left-to-right and right-to-left. 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, 28th Apr 2011 Abstract: We introduce, assuming only a modest background in one variable complex analysis, the rudiments of in finite 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: CDSC-CARMA-CISRA afternoon Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 12:00 pm, Wed, 20th 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, 14th 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 Douglas-Rachford 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 Schramm-Loewner Evolution Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:30 pm, Thu, 7th Apr 2011 Abstract: The stochastic Loewner evolution (SLE) is a one-parameter 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 two-dimensional 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, self-avoiding walk, loop-erased 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: Prof Cristian Calude, Department of Computer Science, The University of Auckland Title: Is quantum randomness pseudo-randomness? Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 31st Mar 2011 Abstract: This talk will present recent theoretical and experimental results contrasting quantum randomness with pseudo-randomness. [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, 15th 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 high-performance 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, 4th 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 Cox-Ross risk-neutral 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 by-product 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, 3rd 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 Cox-Ross risk-neutral 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 by-product 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, 24th 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, 24th 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, 10th 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, data-driven 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 data-centric 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, 8th 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 cross-layer 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: Short-Term Revenue Management: Optimal Targeting of Customers for a Last-Minute Offer Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Mon, 7th Feb 2011 Abstract: We discuss a short-term 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 last-minute 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, 27th 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, 13th 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 Speaker: Prof Giles Auchmuty, Department of Mathematics, University of Houston Title: Variational Principles for Self-adjoint Eigenvalue Problems Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 9th Dec 2010 Abstract: This talk will describe a number of di erent variational principles for self-adjoint eigenvalue problems that arose from considerations of convex and nonlinear analysis. First some unconstrained variational principles that are smooth analogues of the classical Rayleigh principles for eigenvalues of symmetric matrices will be described. In particular the critical points are eigenvectors and their norms are related to the eigenvalues of the matrix. Moreover the functions have a nice Morse theory with the Morse indices describing the ordering of the eigenvector. Next an unconstrained variational principle for eigenfunctions of elliptic operators will be illustrated for the classical Dirichlet Laplacian eigenproblem. The critical points of this problems have a Morse theory that plays a similar role to the classical Courant- Fischer-Weyl minimax theory. Finally I will describe certain Steklov eigenproblems and indicate how they are used to develop a spectral characterization of trace spaces of Sobolev fundtions. [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, 25th 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 two-phase flow in complex pourous media systems Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 2:00 pm, Wed, 24th Nov 2010 Abstract: In this talk we consider two-phase flow models in porous media as they occur in several applications like oil production, pollute transport or CO2-storage. After a general introduction, we focus on an enhanced model where the capillary pressure is rate-dependent. 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, 18th Nov 2010 Abstract: What is a {\em random subgroup} of a group, and who cares? In a (non-abelian) 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, 11th 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 non-increasing 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 Arithmetic-Geometric Mean Continued Fractions and Dynamics Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 4th 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 arithmetic-geometric mean relation and elegant links with elliptic-function 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, 28th 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 k-set or l-set 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, 27th Oct 2010 Abstract: We discuss the feasibility pump heuristic and we interpret it as a multi-start, 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, 21st Oct 2010 Abstract: The Matching Polynomial is a topic in the area of mathematics, statistical physics (dimer-molomer 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, 15th 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 similar-looking symbols. Many writers are unfamiliar with the symbols they must use and therefore write them incorrectly. Mathematical notation is two-dimensional 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 well-segmented. 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, 14th Oct 2010 Abstract: The log-concavity 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 m-fold log-concavity 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 log-concave. In particular, we report on a recent result of Branden which implies infinite log-concavity of the binomial coefficients and other new developments. Examples and conjectures are promised. A PDF of the talk is available here. [Permanent event link] 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, 11th Oct 2010 Abstract: There are many algorithms with which linear programs (LPs) can be solved (Fourier-Motzkin, 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) mixed-integer 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. [Permanent event link] 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, 7th 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. [Permanent event link] 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, 23rd 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. [Permanent event link] CARMA COLLOQUIUM Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 16th Sep 2010 Please note that there is no CARMA Colloquium this week. [Permanent event link] 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, 2nd 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 (F-P) 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 (G-M-Z) 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 non-separable spaces? In 1994 (C-P) 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. [Permanent event link] 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, 23rd 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 (Radon-Nikod´ym Property). [Permanent event link] 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, 20th Aug 2010 Abstract: In this talk we will focus our attention on certain regularization techniques related to two operations involving monotone operators: point-wise sums of maximal monotone operators and pre-compositions 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 operations--extended 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. [Permanent event link] 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, 19th 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 algorithm-based 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 country-by-country 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Ramanujan's alternative theories of elliptic integrals and generalizations of Catalan's constant Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 12th Aug 2010 Abstract: I will describe the history and some recent research on a subject with a remarkable pedigree. Download: Seminar slides (544 KB) [Permanent event link] 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, 5th 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Dr Bishnu Lamichhane, CARMA, The University of Newcastle Title: Hu-Washizu Formulation Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:00 pm, Thu, 29th Jul 2010 Abstract: The Hu-Washizu formulation in elasticity is the mother of many different finite element methods in engineering computation. We present some modified Hu-Washizu formulations and their performance in removing locking effect in the nearly incompressible elasticity. The stabilisation of the standard Hu-Washizu formulation is used to obtain the stabilised nodal strain formulation or node-based 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. [Permanent event link] CARMA COLLOQUIUM Speaker: Mr Shoham Sabach, Technion, Israel Institute of Technology Title: Bregman Nonexpansive Operators in Reflexive Banach Spaces Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 22nd Jul 2010 Abstract: We study the existence and approximation of fixed points of several types of Bregman nonexpansive operators in reflexive Banach spaces. Download: Presentation (418 KB) [Permanent event link] 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, 15th 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, Brondsted-Rockafellar property, etc. [Permanent event link] CARMA COLLOQUIUM AND SIGMAOPT SEMINAR Speaker: Conjoint Prof Steve Wright, Computer Sciences Department and Wisconsin Institute for Discovery, University of Wisconsin-Madison 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, 24th 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. [Permanent event link] 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, 17th Jun 2010 Abstract: Nonconvex/nonsmooth phenomena appear naturally in many complex systems. In static systems and global optimization problems, the nonconvexity usually leads to multi-solutions 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 Lagrangian-type methods and the modern Fenchel-Moreau-Rockafellar duality theories usually produce the well-known duality gap. It turns out that many nonconvex problems in global optimization and computational science are considered to be NP-hard. In nonlinear dynamics, the so-called 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 Newton-type 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 boundary-value problem might not be minimizers of the associated variational problem. From a dual perspective, the convergence (or non-convergence) 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. [Permanent event link] 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, 10th 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 mutually-singular 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. [Permanent event link]