Mathematics seminars 2003-2005
Below is a list of seminars presented during the years 2003-2005 in the Seminar Program of the then Department of Mathematics (later Department of Mathematical and Statistical Sciences) at La Trobe University's campus in Bendigo, Victoria.
Inequalities Day – Three seminars on inequalities were presented on Monday 19 December 2005, as follows.
Bill Helton
Inequalities on polynomials with matrix variables, by Bill Helton (University of California, San Diego)
Scheduled: 11.00 am, Monday 19 December 2005, in Room B1.29
Abstract: Many problems in control and systems engineering, and in an expanding number of areas, directly convert to collections of matrix inequalities. If these are collections of convex or (better yet) collections of linear matrix inequalities, then they are amenable to reliable numerical solution. To get matrix inequalities into such a form requires trickery and often much cleverness. The talk will describe progress on theory underlying how one might make this mystical process systematic.
There is a classical theory of positive polynomials on Rn going back to Hilbert's 17-th problem which concerns the expression of positive polynomials as a sum of squares; it initiated the subject called real algebraic geometry. What is needed for matrix inequalities is a corresponding theory for polynomials in n-noncommuting variables whose properties we test by plugging in n-tupples of matrices; such values of polynomials are matrices. A "positive" noncommuting polynomial is one which always takes positive semidefinite matrix values. Which ones are sums of squares? An analogous notion of convexity for a noncommutative polynomial is common (and important) in systems engineeering. Can we classify them? The talk will describe the beginnings of a noncommutative real algebraic geometry which settles the problems described above.
Alex Rubinov
Abstract convexity with application to global optimization and inequalities, by Alex Rubinov (University of Ballarat)
Scheduled: 12 noon, Monday 19 December 2005, in Room B1.29
Abstract: Development of a theory of global optimization is one of the most challenging problems of modern optimization theory. Currently there are tractable conditions for a global optimum only for very narrow classes of problems, including convex problems. Calculus is not suitable for investigation of global optima, so some new techniques should be invented. One of them is abstract convexity. Recall that a lsc function is convex if and only if this function can be represented as the upper envelope of a set of affine functions. Replacing affine functions with another set of sufficiently simple functions we get abstract convex functions with respect to this set. In this talk I will discuss some main ideas of abstract convexity and application of abstract convexity to examination of global optimality conditions and some inequalities.
Sever Dragomir
Reverse inequalities for vectors and linear operators in Hilbert spaces, by Sever S. Dragomir (Victoria University, Melbourne)
Scheduled: 2.00 pm, Monday 19 December 2005, in Room B1.29
Abstract: The purpose of this talk is to survey recent results due to the author concerning reverses of the Schwarz inequality in real or complex inner product spaces that generalise the classical inequalities due to Polya-Szego (1925), Cassels (1955), Greub-Reinboldt (1959), Shisha-Mond (1967) and Klamkin-McLenaghan (1977). These results are then employed to provide various reverses for the numerical radius of bounded linear operators in complex Hilbert spaces under appropriate norm restrictions.
Zdenek Ryjacek
Closure concepts and stability of graph properties and graph classes, by Zdenek Ryjacek (University of West Bohemia, Pilsen, Czech Republic)
Scheduled: 12 noon, Monday 12 December 2005, in Room B2.05
Abstract: Closure techniques are a powerful tool in studying hamiltonian properties of graphs. In this talk, two closure concepts will be observed, namely, the Bondy-Chvátal closure based on degree sum of pairs of independent vertices, and the closure concept in claw-free graphs based on local completions of neighborhoods of locally connected vertices, introduced by the speaker. Behavior of several hamiltonian-type graph properties with respect to these closure concepts will be studied. Some open questions will be also mentioned.
Mark Mackay
Compartmental Modelling and Health: Learnings from Research on the Application of Compartmental Models for Modelling Bed Occupancy, by Mark Mackay (Department of Health, South Australia)
Scheduled: 12 noon, Friday 14 October 2005, in Room B2.30
Abstract: The use of compartmental models to describe bed occupancy was initiated by Millard and Harrison using geriatric data from the United Kingdom. The potential to improve strategic decision-making in relation to acute care provision in Australia was identified as a result of a bid for substantial additional resources by a hospital on the basis of needing to fund extra beds without any mechanism to support the bid. This presentation will detail the reasons for considering the use of the compartmental model, the validation of its use in acute care setting using Australian and New Zealand data, and some suggested modification of the model. Discussion about impediments for adoption of alternative models will be provided as well as opportunities that should encourage the use of better decision-making in the near future.
Bruce Berndt
Ramanujan's Life and Notebooks, by Professor Bruce Berndt (University of Illinois at Urbana-Champaign) – Professor Berndt is the 2005 Mahler Lecturer of The Australian Mathematical Society
Scheduled: 12 noon, Friday 7 October 2005, in Room B2.30
Abstract: Ramanujan was born in southern India in 1887 and died there in 1920 at the age of 32. He had only one year of college, but his mathematical discoveries, made mostly in isolation, have made him one of this century's most influential mathematicians. An account of Ramanujan's life will be presented. Most of Ramanujan's mathematical discoveries were recorded without proofs in notebooks, and a description and history of these notebooks will be provided. The lecture will be accompanied by overhead transparencies depicting Ramanujan, his home, his school, his notebooks, and those influential in his life, including his mother and wife.
An article about the seminar, titled "Studying a maths genious (sic) at Bendigo", appeared in the Bendigo Weekly newspaper of Friday September 30, 2005.
Jason Giri
Finding the Low Points: A Journey Through Constrained Nonconvex Minimisation, by Jason Giri (University of Ballarat)
Scheduled: 12 noon, Friday 16 September 2005, in Room B2.30
Abstract: Constrained nonconvex optimisation is a field of mathematics which hopes to provide general techniques for solving a large class of practical optimisation problems. Unfortunately, most of these problems are very difficult to solve because they exhibit qualities such as nonsmoothness or multiple constraints along with their nonconvexity. In this seminar I will discuss some of the current minimisation techniques which I have investigated in my PhD thesis and give an overview of their strengths and weaknesses. The seminar will culminate with the presentation of a solution for the well-known Rosen-Suzuki function which improves on that previously published in the literature.
Joe Ryan
The train marshalling problem, by Dr Joe Ryan (University of Ballarat)
Scheduled: 12 noon, Friday 26 August 2005, in Room B2.30
Abstract: The problem considered in this paper arose in connection with the rearrangement of railroad cars in China. In terms of sequences, the problem reads as follows.
Train marshalling problem: Given a partition S of {1,
2, …, n} into disjoint sets S1, S2,
…, St, find the smallest number
The sequence of numbers 1,2,…,n, 1,2,…,n,
… , 1,2,…,n, where the interval 1,2,…,n
is repeated k times, contains all the elements of
Gary Bloom
Crossing numbers, EODERMDROMEs, and the authenticity of Shakespeare's work, by Professor Gary Bloom (City College and the Graduate Center of the City University of New York)
Scheduled: 12 noon, Friday 19 August 2005, in Room B2.30
Abstract: A major technique in linguistics for attributing authorship of Shakespeare's work and other early writings (before copywriting) has been counting word frequencies in the work in question. This seems overly crude to us. We also questioned whether there was an "easy" way to distinguish between languages, other authors, styles of writing, etc.
We chose a type of graph, spelling nets, that are easily generated by text and then chose a graph parameter, crossing number, that we hoped would capture the essential differences in comparitive texts. We discuss why, after writing our third published paper in this area, we realized that we failed.
The silver lining that remained is an intriguing word game of the easy-to-state-but-moderately-hard-to-solve variety. We show a number of solutions in English and various other languages, and we show how even this game gives rise to a number of unanswered quesitons.
Finally, we return to the original questions and consider some more recent work that shows promise for answering our original questions.
Terry Mills
Lost in Space, by Professor Terry Mills (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 29 July 2005, in Room B2.30
Abstract: If you were to step out into space, and wander around randomly, what are the chances that you would return to your starting point?
The answer depends on the space!
In this lecture, I will discuss a classical result of Georg Pólya (1921) in the theory of random walks.
John Crossley
What is mathematical logic?, by Professor John Crossley (Monash University)
Scheduled: 12 noon, Friday 3 June 2005, in Room B2.30 [This seminar is presented jointly with the Department of Computer Science and Computer Engineering.]
Abstract: Mathematical logic is the application of mathematical techniques to logic.
What is logic? I believe I am following the ancient Greek philosopher Aristotle when I say that logic is the (correct) rearranging of facts to find the information that we want.
This involves looking at syntax and semantics. Syntax is how we say things; semantics is what we mean. It should be quite surprising that a few basic rules suffice to yield all those syntactic expression that are always true – and no others.
Next we consider the variety of logics there now are.
We then turn to other parts of mathematical logic: computable or recursive functions, set theory and proof theory.
All of these developments from virtually nothing have taken place over little more than a century.
Christopher Lenard
Tutte's Flow Conjectures: Beyond the Four Colour Theorem, by Dr Christopher Lenard (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 27 May 2005, in Room B2.30
Abstract: About 30 years ago the Four Colour Theorem (for planar graphs) was proved by a computational examination of thousands of special cases: today we seem to be no nearer a "short" proof.
Tutte's Flow Conjectures are set in a framework which exploits the duality between colouring faces of a map and colouring edges in a graph, and so these conjectures are a natural extension of ideas surrounding the Four Colour Theorem.
A flow on a graph is an integer weighting of the (directed) edges in such a way that Kirkhoff's laws are obeyed at each vertex, while a k-flow is a flow in which the weights are chosen from
Four Colour Theorem: Every planar graph is face-4-colourable, and equivalently, every bridgeless planar graph admits a nowhere-zero 4-flow.
Eliminating the constraint of planarity leads to the first of Tutte's conjectures:
5-flow Conjecture: Every bridgeless graph admits a nowhere-zero 5-flow.
In this talk we will survey the ideas surrounding this and various other of Tutte's conjectures.
Grant Cairns
Classification of a special family of graded Lie algebras, by Associate Professor Grant Cairns (La Trobe University, Bundoora)
Scheduled: 12 noon, Friday 20 May 2005, in Room B2.30
Abstract: We classify those finite dimensional Lie algebras which have a basis x1,...,xn with the following properties:
- [xi, xj] = ci, j xi+j for some constants ci, j ,
- c1, j is not zero, for all 1<j<n.
It turns out that there are only 6 such algebras of dimension n<7. In each of the dimensions 7,8,9,10,11, there are infinitely many algebras, while in dimension n>11, there are precisely 4 or 5 algebras, according to whether n is even or odd respectively. This is joint work with Barry Jessup (University of Ottawa).
George Grätzer
Representing finite distributive lattices as congruence lattices of lattices, by Professor George Grätzer FRSC (University of Manitoba, Canada)
Scheduled: 2.30 pm, Friday 13 May 2005, in Room B2.27
Abstract: In 1942, R. Dilworth proved the following theorem: Every finite distributive lattice D can be represented as the congruence lattice of a finite lattice L.
We want: Every finite distributive lattice D can be represented as the congruence lattice of a "nice" finite lattice L.
In 1960, G. Grätzer and E. T. Schmidt proved this with nice = sectionally complemented.
We shall review this field discussing, in addition, nice = semimodular, "small", uniform, isoform, and so on.
Simon Smith
Lebesgue Constants – from Bendigo to Budapest, by Associate Professor Simon Smith (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 15 April 2005, in Room B2.30
Abstract: Lagrange interpolation is a well-known method for approximating a continuous function by a polynomial that agrees with the function at a number of chosen points (the "nodes"). However, the accuracy of the approximation can be greatly influenced by the location of these nodes.
In this talk I will explain why the Lebesgue constant is a useful way to measure a given set of nodes to determine whether its Lagrange polynomials are likely to provide good approximations. There will then be discussion of methods and results for the calculation of Lebesgue constants for some particular node systems and for a weighted interpolation method. Some of these methods and results are classical, while others follow from research carried out recently in Bendigo and while I was on OSP leave in Budapest.
John Schutz
A System of Axioms for Hyperbolic Geometry, by Associate Professor John Schutz (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 18 February 2005, in Room B2.32
Abstract: Three-dimensional hyperbolic geometry is characterized using axioms of order, incidence, dimension, continuity and, instead of an axiom of parallels, there is an axiom of "rigidity" and, rather than several axioms of congruence, there is one axiom of symmetry. It is claimed that this system of axioms is simpler than previous systems of axioms. If people are interested and if time permits, I will also discuss a characterisation of ellipsoids in projective geometry by a property of isotropy about a single point.
Bob Anderssen
Playing Mathematics with the Stuart Piano, by Dr Bob Anderssen (CSIRO Mathematical and Information Sciences, Canberra)
Scheduled: 12 noon, Friday 12 November 2004, in Room B2.30
Abstract: Prior to 1800, the vibrating length of a string on a piano copied the arrangement on the harpsicord. One end of the vibrating length was determined by an 11 degree bend through a horizontal degree zig-zag clamp attached to the bridge on the soundboard. The other end was determined by an 11 degree bend around a fixed pin located between the de Capo bar and the tuning pin. This primitive arrangement was effective for the relatively gentle plucking motion of the harpsicord, but was unable to retain the strings in the proper position under the more powerful blows of the piano's hammer action. During the first decade of the 1800's, the famous piano and harp maker Erard of Paris, invented a brass stud (agraffe (staple)) with holes drilled through it to accommodate the triple, double or single strings of the tricords, bicords and the monocords. A thread on the base of the agraffe allowed it to be rigidly attached to the piano frame. By firmly resisting the upward motion of the hammer blow, the agraffe was an immediate success and central to the subsequent success of the piano as a musical instrument. It allowed the vibrations of the speaking length to radiate a clearer tone and a fuller sound with reduced impact noise. During the 19th and early 20th centuries, various attempts were made to duplicate this more rigid clamping system on the bridge. Expensive, but cumbersome, vertical zig-zag systems were found to give superior results. However, the cheaper and simpler historic system retained its dominance. The Australian piano maker, Wayne Stuart, commenced his search for a less expensive and more functional solution in the mid-1970's which resulted in his vertical zig-zag innovation of the late 1980's. (This is a excellent example of how long the innovative step that solves the specifics of a problem can lag behind the good idea on which it is based.) The new (grand) pianos that utilize the Stuart clamping are manufactured by Piano Australia Pty Ltd in Newcastle with the brand name Stuart & Sons. These pianos, as a direct consequence of the clamping, have an extradordinary clarity of tone, increased sustain and lower inharmonicity, when compared with the traditional grand pianos. Interestingly, for a rigorous explanation of the difference between horizontal and vertical zig-zag clamping, one must turn to an analysis of the non-linear vibrating string equation.
Peter Sullivan
Students' perceptions of factors contributing to successful participation in mathematics, by Professor Peter Sullivan, Dr Steve Tobias and Assoc Prof Vaughan Prain (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 22 October 2004, in Room B2.30
Abstract: This seminar is a report of a project investigating students' perceptions of the extent to which their own efforts influence their achievement at mathematics and their life opportunities. We conducted two hour interviews with over 50 students, as well as collecting other data. Even students who were confident, successful and persistent exhibited short term goals. It also seems that classroom culture may be an important determinant of under participation in schooling.
Vincent Rouillard
The use of intrinsic mode functions to characterise shocks and vibrations in the distribution environment, by Vincent Rouillard (School of Architectural, Civil and Mechanical Engineering, Victoria University)
Scheduled: 12 noon, Friday 15 October 2004, in Room B2.30
Abstract: This paper describes an innovative approach, based on the Instrinsic Mode Functions (IMF), to characterise the nature of mechanical shocks and vibrations encountered in transport vehicles. The paper highlights the importance of understanding the nature of transport shock and vibrations and shows that their accurate characterisation is essential for the optimisation of protective packaging. Although there have been numerous studies aimed at characterising random vibrations during transport, the majority of those have been limited to applying relatively conventional signal analysis techniques such as the average Power Spectral Density (PSD) for vibration data and probability distribution estimates for shock data. This paper investigates the benefits offered by the recently introduced Hilbert-Huang Transform when characterising non-stationary random vibrations in comparison with more traditional Fourier analysis based techniques. The paper describes the operation of the Hilbert-Huang Transform which was developed to assist in the analysis of non-Gaussian and non-stationary random data. The Hilbert-Huang transform is based on the Empirical Mode Decomposition technique used to produce a finite number of Intrinsic Mode Functions (IMF), which, as a set, provides a complete description of the process. It is shown how these Intrinsic Mode Functions are well suited to the application of the Hilbert transform to determine the magnitude and instantaneous frequency of each Intrinsic Mode Function. The technique is applied to various records of random vibration data collected from transport vehicles in order to illustrate the benefits of the method in characterising the nature of non-stationarities present in transport vibrations.
Terry Mills
How to draw a histogram, by Professor Terry Mills (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 8 October 2004, in Room B2.30
Abstract: The histogram is a simple graph that describes a statistical distribution, such as the age distribution of a population. The histogram conveys information readily, it is easy to read, and is one of the first ideas encountered in high school statistics. However, authors of elementary statistics books tend to skate over details about the question "How do you draw a histogram?". As is often the case, asking a simple question about a basic idea is like opening Pandora's box. In this seminar, we will see what is in the box!
Mirka Miller
New Results in the Topology of Interconnection Networks as Modelled by Graphs, by Mirka Miller (Professor of Computer Science, University of Ballarat)
Scheduled: 12 noon, Friday 24 September 2004, in Room B2.30
Abstract: Networks govern all aspects of society, including transportation, communication networks, computer networks, social networks, and networks for the distribution of goods etc. - and the theoretical analysis of such networks has become a subject of fundamental importance. Networks can be modelled by graphs.
Such a network (graph) consists of a number of nodes and some connections (either unidirectional or bidirectional) between nodes. An interesting measure related to the performance of a network is its diameter which is the maximum distance between any two nodes of the network. Given a limited number of connections (degree) available at any node and given the desired value of the network's diameter, the following problem has been of interest:
Degree/diameter problem: Given maximum degree and diameter, what is the largest possible number of nodes in a network?
In this talk we give an overview of the degree/diameter problem and we present some recent new results.
Angela Pezic
Modelling Internal Migration in Bendigo and Warrnambool, by Ms Angela Pezic (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Thursday 9 September 2004, in Room B1.30
Abstract: In many Australian regional centres, internal migration is the principal influence on population growth. In this paper we explore some of the determinants of internal migration using the most recent census data with attention restricted to the regional centres of Bendigo and Warrnambool in Victoria. To facilitate this we use geographically weighted regression (GWR) to estimate the effect of factors such as age, unemployment, housing affordability and other socio-economic variables on the internal migration measure. A major advantage of GWR over the traditional (global) regression methods is that it provides spatially varying estimates of model parameters. The resulting parameter spaces can then be thematically mapped thus providing a useful graphical representation of spatially varying relationships. For example, a somewhat surprising result of our work is found in the effect of relative house price on in-migration to Bendigo. The thematic map of the house price parameter space shows that an increase in house prices (relative to Bendigo) in some northern and central Victorian areas has a positive effect on the in-migration measure. However for other areas and in particular, metropolitan areas, the effect is much smaller. This observation seems to run counter to the "conventional wisdom" of some in local government and the regional media who predict an influx of residents who, upon selling their metropolitan home, settle in regional centres using the residual of their asset to fund retirement.
Pietro Cerone
On bounds for the Euler zeta function, by Assoc Prof Pietro Cerone (School of Computer Science and Mathematics, Victoria University)
Scheduled: 12 noon, Friday 27 August 2004, in Room B2.09
Abstract: Accurate bounds are obtained for estimating the Euler zeta function at odd integer values in terms of known zeta function values at even integers. This is accomplished from an identity involving the zeta function at a distance of one apart. Upper bounds for odd Euler zeta functions are also obtained using a technique involving the Chebyshev functional.
Theo Tuwankotta
Coupled oscillators with widely separated frequencies and energy-preserving nonlinearity, by Dr J. M. Tuwankotta (A.R.C. Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics, La Trobe Unversity, and Mathematics Department, Bandung Institute of Technology, Indonesia)
Scheduled: 1 pm, Friday 13 August 2004, in Room B2.09
Abstract: We present an analysis of a system of coupled oscillators suggested by atmospheric dynamics. We assume two conditions to be satisfied by the system. The first is that the frequencies of the characteristic oscillations are widely separated. The second is that the nonlinear part of the vector field preserves the energy which is represented by the distance to the origin. Using normal form theory, we have contructed an approximation for the system. Due to the nature of the problem, the normal form can be seen as an sphere-preserving three-dimensional system which is linearly perturbed. Finally, we present some numerical bifurcation analysis of the three dimensional system.
John Schutz
Non-Euclidean geometry and space-time, by Assoc Prof John Schutz (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Thursday 5 August 2004, in Room B2.30
Abstract: During my recent Outside Studies Program which involved visits to the Australian Mathematical Sciences Institute, the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) and the Technical University of Braunschweig, I investigated non-Euclidean geometry and space-time structure. In one completed article, ellipsoids are characterised in projective geometry by the property of isotropy. This result is then used in a second article to present a particularly simple system of axioms for hyperbolic geometry. The investigations into space-time structure are continuing. In the seminar, aspects of these geometries and results will be presented so as to be accessible to a general audience.
Graeme Byrne
Internal Migration and Regional Population Growth, by Dr Graeme Byrne and Ms Angela Pezic (Department of Mathematics, La Trobe University, Bendigo)
Scheduled: 12 noon, Thursday 10 June 2004, in the Lecture Theatre, Ironbark Centre [This seminar is also part of the Seminar Program of the School of Business and Technology.]
Abstract: In regional centres such as Bendigo the main determinant of population growth is internal migration. Unlike natural growth, internal migrants present local government with special problems due to their demographic characteristics. In this talk we examine the most recent census data and report on some of these characteristics as well as discuss the likely implications for Bendigo and its satellite communities. We also explore a new method of estimating the effect of factors such as age, unemployment and housing affordability on internal migration.
Dr Graeme Byrne is a Senior Lecturer and Ms Angela Pezic is a Doctoral student working on a demographic project whose methods and conclusions will have interesting implications for town planning and the provision of urban and social infrastructure.
Terry Mills
A Mathematician Goes to Hospital, by Professor Terry Mills (Department of Mathematics, Faculty for Regional Development, La Trobe University, and Collaborative Health Education and Research Centre, Bendigo Health Care Group)
Scheduled: 12 noon, Thursday 25 March 2004, in Room B2.28-29 [This seminar is also part of the Seminar Program of the School of Business and Technology.]
Abstract: La Trobe University, Bendigo is a key component in the University's effort to realise its mission in regional engagement. In recent years, our Faculty has developed a strong focus on encouraging interaction between La Trobe University and regional Victoria. While it is easy to imagine how academics in some disciplines could contribute to community-university interaction, it is more difficult to imagine how those in other disciplines (such as mathematics) can be so involved. As a mathematician in the Faculty for Regional Development, I have chosen to make a contribution to health care in the region. Over the last five years I have been able to blend my skills as an academic mathematician with the needs of the Bendigo Health Care Group (BHCG). In this presentation I will describe the projects at BHCG in which I am involved, and their impact on my work in undergraduate teaching, course development, and research. Also, I will mention some challenges associated with community engagement and the key factors that have led to my experience being both exciting and rewarding.
Baorui Song
Topics in Rational Interpolation, by Associate Professor Baorui Song (Shanghai Jiao Tong University, China)
Scheduled: 12 noon, Friday 24 October 2003, in Room B2.15
Abstract: In this seminar, I will talk about the definition and basic properties, numerical algorithms and the convergence problems of rational interpolation. Some generalizations and applications of rational interpolation are briefly mentioned.
Daniel Alpay
Reproducing Kernel Hilbert Spaces and the Theory of Linear Systems, by Professor Daniel Alpay (Ben-Gurion University of the Negev, Israel)
Scheduled: 12 noon, Friday 10 October 2003, in Room B2.15
Abstract: In this seminar, I will review the relationships between the theory of linear systems and reproducing kernels. Then we can discuss a related inverse scattering problem. I will also explain how the reproducing kernel approach allows one to tackle more general situations such as non-stationary systems.
Ashley Dyson
Quadratic Equations, by Ashley Dyson (Girton Grammar School, Bendigo)
Scheduled: 12 noon, Friday 15 August 2003, in Room B2.15
Abstract: Ashley has been a work experience student in the Department of Mathematics for the past fortnight. During this time, he has been investigating quadratic equations, including their history, applications, and connections with other areas of mathematics. In this seminar he will present some of his findings.
Hendrik Lenstra
Coin-flipping by Telephone, by Professor Hendrik Lenstra (Universiteit Leiden, The Netherlands, and University of California, Berkeley) – Professor Lenstra is the 2003 Mahler Lecturer of The Australian Mathematical Society
Scheduled: 12 noon, Monday 30 June 2003, in Room B2.15
Abstract: This conveys the essential point of applying number theory to cryptography to a perfectly general mathematical audience. True math, but elementary and expository.
Hendrik Lenstra, who holds appointments at the University of California at Berkeley, and the University of Leiden, the Netherlands, is widely regarded as the world's premier algorithmic number theorist. He is responsible for two of the most famous algorithms in 20th century number theory: the LLL lattice basis reduction algorithm (along with his brother, Arjen Lenstra, and Laszlo Lovasz) and the elliptic curve factoring algorithm.
Jason Giri
The Convoluted World of Optimization, by Jason Giri (University of Ballarat)
Scheduled: 11 am, Friday 27 June 2003, in Room B1.30
Abstract: The field of constrained mathematical optimization is one of the most practically applicable areas of mathematics. It has been used successfully to solve problems in a wide range of areas including economics, communications and computational chemistry. A key technique in the solution of many of these types of problems is the method of Lagrange multipliers. This elegant and powerful method has been used since the eighteenth century, but an important generalization which was made around the middle of the twentieth century has significantly extended the utility of the technique. This seminar will discuss the details of these traditional Lagrangian methods and introduce some recent results which generalize the technique even further.
Whole of Hospital Simulation, by Philip Cooper and Christopher Bain (Clinical Epidemiology and Health Service Evaluation Unit, Melbourne Health, and Iridium Consulting, Royal Melbourne Hospital) [Co-author: Don Campbell]
Scheduled: 12 noon, Friday 30 May 2003, in Room B2.30
Abstract: Managing a modern large hospital, which provides a complex range of services, involves optimising patient access, throughput and resource use, and constitutes an enormous challenge. This must be done in the face of increasing demand for emergency and surgical elective patient access and reduced bed availability. In addition, managers face difficulties in attracting and retaining sufficient nurses and escalating health service costs. Inevitably undesirable events occur, which include bed block, ambulance bypass, long waits for elective surgery and elective theatre list cancellations.
There are significant difficulties in planning and instituting changes in a hospital because of flow-on effects that are difficult to predict. In addition, the internal allocation of resources within a hospital is complex to the point where it exceeds human ability to understand the system-wide implications of individual resourcing decisions. In the absence of appropriate data to guide management decision making the "loudest" opinion often prevails when resource allocation decisions are made. The management policies that will optimise the numbers of patients treated and still maintain an acceptable quality of service will demand new approaches to service provision and patient management, based on an understanding of factors affecting optimal movement of patients through a complex dynamic system.
Around the world, potential solutions to the current problems are increasingly drawing on an understanding of hospital systems as dynamic, complex entities. One means of exploring these issues is through simulation modelling. There have been various attempts at modelling some aspects of health care both at institutional and system levels. This talk will outline the development and use of a discrete event simulator at Melbourne Health. It is believed that this is a world first since it models the whole of a hospital, in a significant amount of detail, and can be configured to represent any hospital.
Terry Mills
Reproducing Kernel Hilbert Spaces and Probability, by Professor Terry Mills (La Trobe University, Bendigo)
Scheduled: 12 noon, Friday 28 March 2003, in Room B2.05
Abstract: The theory of reproducing kernel Hilbert spaces was established in a seminal paper by Nachman Aronszajn in 1950. Since then, these spaces have proved to be useful in many different branches of mathematics. In this seminar, I will explain how they arise in probability theory.
Rainer Loewen
Surfaces Supporting Line Geometries, by Professor Rainer Loewen (Technische Universität Braunschweig, Germany)
Scheduled: 12 noon, Friday 21 February 2003, in Room B2.15
Abstract: We suppose we are given a connected surface endowed with a system of curves (the "lines") such that any two distinct points are joined by a unique line, which depends continuously on the pair of points. Also we assume that intersection points exist for an open set of line pairs and again depend continuously on the line pair. We shall give some examples and explain the first steps in the theory of such surface geometries, e.g., why a compact line has to intersect every other line. We outline a proof of the result that the point surface can only be a disk, a Moebius strip, or a sphere with one cross cap (the real projective plane).