• CARMA COLLOQUIUM
• Speaker: Dr Judy-anne Osborn, Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University
• Title: Searching for Maximal Determinant Matrices
• Location: Room V206, Mathematics Building
• Access Grid Venue: UNewcastle [ENQUIRIES]
• Date and Time: Monday, 7^th June, 2010, 3:00 pm
• Abstract:

  The Maximal Determinant problem of Hadamard asks for the largest possible determinant of a square matrix with entries drawn from the set {+1, -1}. The history of this problem begins with Sylvester in 1867, who answered the question in a special case by providing a recursive construction for maximal determinant matrices whose order is a power of two. Powers of two, and more generally, sizes divisible by four, are special in that they are candidates for meeting the upper bound of n^(n/2) stated by Hadamard in 1893. The famous Hadamard Conjecture is the claim that divisibility of the order by four is sufficient as well as necessary for the existence of a matrix with determinant meeting Hadamard's bound. The smallest order for which the conjecture is currently unresolved is 668. The Maximal Determinant problem subsumes the Hadamard Conjecture, but also deals with cases of orders congruent to 1, 2 or 3 modulo 4, into which the remainder of the problem naturally splits. The nature of each of these classes differs sharply, with number theory playing a role and orders congruent to 3 mod 4 turning out the most difficult. Until recently, the smallest order for which the Maximal Determinant question was unresolved was n = 19. I will describe the computer search technique by which this size was recently resolved, as well as visualization of the search space. This is joint work with William Orrick, Richard Brent and Paul Zimmermann.

• CARMA COLLOQUIUM
• Speaker: Dr Sinai Robins, Nanyang Technological University, Singapore
• Title: Polyhedral cones, their theta functions, and what they tell us about polytopes
• Location: Room V129, Mathematics Building
• Date and Time: Thursday, 3^rd June, 2010, 4:00 pm
• Abstract:

  We will first give a general introduction to some ideas in polyhedral combinatorics. Then, we will see that the result of J. Gram gives us a way to relate the solid angles of each face of a polytope to each other, a result that extends (to all dimensions) the 2-dimensional elementary school theorem about sums of angles of a triangle adding up to 180 degrees. We then give a further extension of Gram's theorem, using polyhedral theta functions.

• Slides from Sinai's talk

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Ben Tillman, The University of Newcastle
• Title: Some realisations of configuration spaces
• Location: Room V205, Mathematics Building
• Date and Time: Wednesday, 2^nd June, 2010, 3:00 pm

• SIGMAOPT SEMINAR
• Speaker: Laureate Prof Jonathan Borwein, CARMA, The University of Newcastle
• Title: High-Precision Computation: Mathematical Physics and Dynamics
• Location: Room V206, Mathematics Building
• Access Grid Venue: UNewcastle
• Date and Time: Wednesday, 2^nd June, 2010, 2:00 pm
• Abstract:

  At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort.

  This talk and associated paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the fine structure constant, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic attractors, Ising theory, quantum field theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.

  This is joint work with D. Bailey (Lawrence Berkeley) and R. Barrio (Zaragoza). The paper is available at http://carma.newcastle.edu.au/jon/hpmd.pdf.

• A PDF of the talk is also available.

• CARMA CAT(0) SEMINAR
• Speaker: Ian Benn, The University of Newcastle
• Title: Riemannian geometry
• Location: Room V205, Mathematics Building, Callaghan Campus
• Date and Time: Wednesday, 2^nd June, 2010, 1:00 pm

• CARMA COLLOQUIUM
• Speaker: Dr Sinai Robins, Nanyang Technological University
• Title: When Does an Arithmetic Progression Through an Infinite Sequence Remember the Whole Sequence?
• Location: Room V129, Mathematics Building
• Date and Time: Thursday, 27^th May, 2010, 4:00 pm
• Abstract:

  The Atkin-Hecke U_p operator sifts out every p^th coefficient of a power series of a modular form, where p is any integer. But if we replace the space of modular forms by the space of rational functions, we get a new description of the eigenfunctions. We can think of an eigenfunction F of U_p formally by considering the power series coefficients of F as a sequence of complex numbers such that if we pick every p^th one, we get the original sequence back again, up to a constant multiple. When F belongs to the space of Hypergeometric series, to get an interesting classification of eigenfunctions again. These processes seem to build up - from first principles - a lot of mathematics, including some delicate estimates of exponential sums by Bourgain and Mei Chu. We will discuss the current state of knowledge in this field and pose some open questions.

• Slides from Sinai's talk

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Wadim Zudilin, The University of Newcastle
• Title: Super Congruences
• Location: Room V205, Mathematics Building
• Date and Time: Wednesday, 26^th May, 2010, 3:00 pm

• CARMA CAT(0) SEMINAR
• Speaker: Miroslav Bacak, The University of Newcastle
• Title: Riemannian Manifolds and Their Curvature
• Location: Room V205, Mathematics Building, Callaghan Campus
• Date and Time: Tuesday, 25^th May, 2010, 1:00 pm
• Abstract:

  I will present basic facts on Riemannian manifolds with regard to their sectional curvature. The main theorem states that nonpositive sectional curvature is equivalent to CAT(0).

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Matt Skerritt, The University of Newcastle
• Title: A Quick Start guide to Distributed Algorithms
• Location: Room V205, Mathematics Building
• Date and Time: Wednesday, 19^th May, 2010, 3:00 pm

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Ian Searston, The University of Newcastle
• Title: Alternating Projections in CAT(0) Spaces
• Location: Room V205, Mathematics Building
• Date and Time: Tuesday, 18^th May, 2010, 1:00 pm
• Abstract:

  The method of Alternating Projections in Hilbert space has given rise over the years to a number of very useful algorithms. CAT(0) spaces, which include Hilbert spaces, classical hyperbolic spaces, R Trees and Euclidean buildings amongst others, seems a very useful setting for these algorithms.

  To this end, we will prove the convergence of the alternating projection sequences for convex subsets of CAT(0) spaces.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Ian Searston, The University of Newcastle
• Title: Best Proximity Points in Geodesic Metric Spaces
• Pizzas: nil
• Location: Room V205, Mathematics Building
• Date and Time: Tuesday, 11^th May, 2010, 3:00 pm
• Abstract:

  A mapping T: A ∪ B ↦ A ∪ B such that T(A) ⊂ B and T(B) ⊂ A is called a cyclic map, and a point x such that d(x,Tx) = dist(A,B) is called a proximity point for T. We will survey some recent results is this area including the existence and uniqueness of best proximity points in geodesic metric spaces.

• CARMA COLLOQUIUM
• Speaker: Wadim Zudilin, The University of Newcastle
• Title: Dedekind's eta Function and Rogers-Ramanujan Identities
• Location: Room V129, Mathematics Building
• Date and Time: Thursday, 6^th May, 2010, 4:00 pm
• Abstract:

  The talk is based on joint work with Ole Warnaar. We prove a q-series identity that generalises Macdonald's A_2n⁽²⁾ eta-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalise even further to also include the Andrews-Gordon identities.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Ian Searston, The University of Newcastle
• Title: Best Proximity Points in Geodesic Metric Spaces
• Pizzas: nil
• Location: Room V205, Mathematics Building
• Date and Time: Tuesday, 4^th May, 2010, 3:00 pm
• Abstract:

  A mapping T: A ∪ B ↦ A ∪ B such that T(A) ⊂ B and T(B) ⊂ A is called a cyclic map, and a point x such that d(x,Tx) = dist(A,B) is called a proximity point for T. We will survey some recent results is this area including the existence and uniqueness of best proximity points in geodesic metric spaces.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Jim MacDougall, The University of Newcastle
• Title: Rational Tetrahedra
• Location: Room V205, Mathematics Bldg, Uni of Newcastle
• Date and Time: Wednesday, 28^th April, 2010, 3:00 pm

• CARMA CAT(0) SEMINAR
• Speaker: Jon Borwein, The University of Newcastle
• Title: Alternating Projections in Hilbert Spaces II
• Pizzas: BYO
• Location: Room V205, Mathematics Building, Callaghan Campus
• Date and Time: Tuesday, 27^th April, 2010, 1:00 pm
• Abstract:

  I will sketch the main ingredients of the theory of Alternating projections in Hilbert space.

• Slides from Jon's talk

• CARMA COLLOQUIUM
• Speaker: Nikolai Kruzhilin, Steklov Mathematics Institute, Russian Academy of Sciences
• Title: Holomorphic Naps of Reinhardt Domains
• Location: Room V129, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: Thursday, 22^nd April, 2010, 4:00 pm
• Abstract:

  A domain in Cⁿ which is stable under rotations of coordinate variables is called a Reinhardt domain. Holomorphic automorphisms and holomorphic maps of Reinhardt domains are discussed.

• CARMA CAT(0) SEMINAR
• Speaker: Miroslav Bacak, The University of Newcastle
•     Title: Weak Topology on CAT(0)
• Speaker: Jon Borwein, The University of Newcastle
•     Title: Alternating Projections in Hilbert Spaces
• Pizzas: Chicken Italiano, Capriciosa, Toni Pepperoni
• Location: Room V205, Mathematics Building, Callaghan Campus
• Date and Time: Tuesday, 20^th April, 2010, 1:00 pm
• Abstract:

  Miroslav will recall the notion of the weak convergence in CAT(0) spaces and then Jon will overview the most important results on the Alternating Projection Method in Hilbert spaces.

• Slides from Miroslav's talks (including previous CAT(0) seminars)
• Slides from Jon's talk

• CARMA COLLOQUIUM
• Speaker: Brian Alspach, The University of Newcastle
• Title: Three Hamilton Decomposition Problems
• Location: Room V129, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: Thursday, 15^th April, 2010, 4:00 pm
• Abstract:

  I shall discuss three middle-aged problems dealing with decomposing graphs into Hamilton cycles. There will be something old, something new, something borrowed, and something blue.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: O-Yeat Chan, The University of Newcastle
• Topic: Box Integrals
• Location: Room V205, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: Wednesday, 14^th April, 2010, 3:00 pm

• CARMA CAT(0) SEMINAR
• Speaker: Dr Miroslav Bacak, The University of Newcastle
• Title: Euclidean Buildings
• Pizzas: Supreme, Godfather, Fire Breather
• Location: Room V205, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: Tuesday, 13^th April, 2010, 1:00 pm
• Abstract:

  The Euclidean building is an important example of a CAT(0) space. I will give definitions of simplicial complex, Euclidean building, and related objects. Then I will show that Euclidean buildings are CAT(0).

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Laureate Prof. Jon Borwein, The University of Newcastle
• Topic: Multiple Zeta Values
• Location: Room V205, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: Wednesday, 31^st March, 2010, 3:00 pm

• CARMA CAT(0) SEMINAR
• Speaker: Dr Miroslav Bacak, The University of Newcastle
• Title: Metric Projections onto Convex Sets
• Pizzas: Hawaiian, Toni Pepperoni, Meatosaurus
• Location: Room V129, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: Tuesday, 30^th March, 2010, 1:00 pm
• Abstract:

  I will prove the main theorem on projections and mention some related results. We may also discuss miscellaneous issues (e.g. cosine law) according to your taste..

• CARMA COLLOQUIUM
• Speaker: Dr Miroslav Bacak, The University of Newcastle
• Title: Weak Topology on CAT(0) Spaces
• Location: Room V129, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: Thursday, 25^th March, 2010, 4:00 pm
• Abstract:

  The talk focuses on metric spaces of non-positive curvature, called CAT(0) spaces. These include complete simply connected Riemannian manifolds of non-positive sectional curvature, R-trees, Hilbert spaces, Euclidean buildings, and hyperbolic spaces.

  We shall introduce a new topology on CAT(0) spaces which induces a type of weak convergence, known in fixed point theory as delta convergence.

• CARMA COLLOQUIUM
• Speaker: Laureate Prof. Jon Borwein, The University of Newcastle
• Title: 32 Goldbach Variations
• Location: Room V129, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: Thursday, 19^th March, 2010, 4:00 pm
• Abstract:

  We give thirty-two diverse proofs of a small mathematical gem -- the fundamental Euler sum identity

  ζ(2,1) = ζ(3) = 8 &zeta(2,1).

  We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.

• CARMA COLLOQUIUM
• Speaker: Prof. George Willis, The University of Newcastle
• Title: Is Time Necessary?
• Location: Room V129, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: Thursday, March 11^th, 2010, 4:00 pm
• Abstract:

  There are many cases in mathematics where an object or structure that is used in applications turns out to be 'logically necessary' in the sense of L. Pontryagin. The case that Pontryagin had in mind was that of the fields of real and complex numbers: in applications we make use of their algebraic operations together with the topological properties that they are connected, complete, locally compact spaces and it turns out that these two fields are only mathematical structures that possess all of these properties. This talk will discuss another case of 'logical necessity' that might arise in the study of Banach algebras and their applications. Signal processing may be modelled by convolution operators over the natural numbers in the case of discrete time and the positive real numbers in the case of continuous time. Convolution operators are analyzed using the Laplace transform technique, which is a particular case of the Gelfand transform of Banach algebra theory. The time parameter makes its presence felt algebraically through the linear ordering of the invariant subspaces of the operator and of the ideals in the associated convolution algebras.

  The talk will review convolution algebras and their use in models, and the relationship between time and the linear ordering of ideals will be explained. (It will also be seen that the convolution operation itself is logically necessary under conditions imposed by the model.) Then a possible approach to extending the Gelfand methods for analyzing Banach algebras will be described. This approach involves defining a class of algebras that are to be the `atoms' for the analysis, and it is conjectured that algebras in this class necessarily have the time-like linear ordering of ideals that is seen in 1-parameter convolution algebras.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: O-Yeat Chan, The University of Newcastle
• Topic: The Quadratic Sieve Factorization Algorithm
• Location: Room V205, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: Wednesday, March 10^th, 2010, 3:30 pm

• CARMA Lecture Series
• Co-sponsored by AMSI
• 
• Speaker: Terry Rockafellar, Department of Mathematics, The University of Washington
• Series Title: THE FUNDAMENTAL QUADRANGLE OF RISK IN OPTIMIZATION AND ESTIMATION
• 
  Three interrelated lectures on an emerging paradigm which connects optimization modeling under uncertainty with new developments in statistics.
• 
  The three lectures detailed below will be available on the access grid ("UNewcastle" venue). This visit is sponsored by AMSI, ANZIAM and CARMA.
• 
  Lecture 1: Quantifications of Risk in Stochastic Optimization
• Location: Room V206 (Access Grid Room), Mathematics Building, Callaghan Campus, The University of Newcastle
• Access Grid Venue: UNewcastle [Technical contact]
• Time: 4:00 - 5:00 pm
• Date: Monday, February 22^nd, 2010
• Abstract: Optimization problems can typically be described as minimizing some kind of "cost" subject to upper bounds on other kinds of "costs". However, in a stochastic environment, decisions do not result in numerical values for the "costs" but in random variables with distributions which can only be shaped by the decisions in one way or another. Preferences toward risk are essential then in answering the question of what should be minimized and what the constraints should be. This leads to a theory of risk quantification in which convex analysis has a major role. Properties of monotonicity and aversity along with convexity distinguish the superior forms of modeling. They point especially to quantifications built around so-called "conditional value-at-risk," which arose in mathematical finance but also suggests the need for rethinking common practices in reliability engineering.
• Seminar 1 slides (PDF, 2.4 MB)
• Seminar 1 notes from whiteboard (PDF, 216 KB)
• 
  Lecture 2: Quantifications of Error in Generalized Regression and Estimation
• Location: Room V206 (Access Grid Room), Mathematics Building, Callaghan Campus, The University of Newcastle
• Access Grid Venue: UNewcastle [Technical contact]
• Time: 4:00 - 5:00 pm
• Date: Wednesday, February 24^th, 2010
• Abstract: Least-squares methodology is traditional in approximating one random variable by a linear combination of other, more accessible random variables. But it is not the only possibility and may not be the best in some circumstances when overestimation may be riskier than underestimation, or the approximation must enter parametrically in a problem of optimization. General axioms for a quantification of error lead to a scheme of regression that centers on a "statistic" and nonstandard "deviation" associated with that quantification. The choices can be tuned then to particular applications, for instance where quantiles or mixed quantiles are more important than mean values.
• Seminar 2 slides (PDF, 312 KB)
• Seminar 2 notes from whiteboard (PDF, 128 KB)
• 
  Lecture 3: Risk Versus Deviation, Regret, and Entropic Duality
• Location: Room V206 (Access Grid Room), Mathematics Building, Callaghan Campus, The University of Newcastle
• Access Grid Venue: UNewcastle [Technical contact]
• Time: 4:00 - 5:00 pm
• Date: Thursday, February 25^th, 2010
• Abstract: A basic correspondence between measures of risk and measures of deviation ties optimization and estimation together. It is echoed by a connection between error and quantifications of "regret" such as have appeared in penalty expressions for constraints in stochastic programming. The fundamental quadrangle of risk is thereby brought to completion. Dualizations of the concepts then provide interesting interpretations involving "generalized entropy".
• Seminar 3 slides (PDF, 808 KB)
• Seminar 3 notes from whiteboard (PDF, --- KB)

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Wadim Zudilin, The University of Newcastle
• Topic: On a q-rious positivity
• Location: Room V205, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: February 24^th, 2010 (Wednesday), 2:30 pm

• CARMA COLLOQUIUM
• Speaker: Randall J. LeVeque, Applied Mathematics Department, University of Washington
• Title: High-Resolution Finite Volume Methods and Applications to Tsunami Modeling
• Location: Room V129, Mathematics Building, Callaghan Campus,
  The University of Newcastle
• Date and Time: February 19^th, 2010 (Friday), 4:00 pm
• Abstract:

  Hyperbolic systems of partial differential equations often arise when modeling phenomena involving wave propagation or advective flow. Finite volume methods are a natural approach for conservation laws of this form since they are based directly on integral formulations and are applicable to problems involving shock waves and other discontinuities. High-resolution shock-capturing methods developed originally for compressible gas dynamics can also be applied to many other hyperbolic systems. A general formulation of these methods has been developed in the CLAWPACK software that allows application of these methods, with adaptive mesh refinement, to a variety of problems in fluid and solid dynamics.

  I will describe these methods in the context of some recent work on modeling geophysical flow problems, particularly in the study of tsunamis. Accurate prediction of their propagation through the ocean and interaction with coastal topography is essential in issuing early warnings and in the study of historical tsunamis. Modeling wave motion at the shore is complicated by the fact that grid cells change between wet and dry as the wave moves in and out. Special Riemann solvers have been developed to deal with dry states in order to capture the shoreline location on a rectangular grid. Propagation of small amplitude waves over deep ocean when the bathymetry varies on much larger scales than the wave amplitude will also cause numerical problems unless the method is properly formulated. Adaptive mesh refinement is desirable in order to allow much greater resolution near the shore than in the open ocean, but introduces new difficulties with varying bathymetry and dry cells. I will describe some recent progress and joint work with David George and Marsha Berger.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Chris Maitland, The University of Newcastle
• Topic: Cinderella
• Location: Room V205, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: February 17^th, 2010 (Wednesday), 2:30 pm

• CARMA COLLOQUIUM
• Speaker: Jerzy A. Filar, Foundation Chair of Mathematics and Statistics, The University of South Australia
• Title: The Hamiltonian Cycle Problem and Some Challenging Non-Convex Programs
• Coauthor: Brailey Sims, University of Newcastle
• Location: Room V129, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: February 11^th, 2010 (Thursday), 4:00 pm
• Abstract:

  We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider the HCP as an optimization problem over the space of state-action frequencies induced by the MDP's stationary policies. In recent years, this approach to the HCP has led to a number of alternative formulations and algorithmic approaches involving researchers from a number of countries including Australia, USA, India, The Netherlands, France, China and Russia.

  In this lecture we focus on approaches involving certain classes of perturbed and unperturbed mathematical programs. One of these is a suitably constructed indefinite quadratic programming problem over a polytope. It is known that whenever a given graph possesses Hamiltonian cycles all global minima of this indefinite program are attained at extreme points of the feasible region induced by these cycles. Also, the nonnegative objective function attains the lower bound of zero at these global minima. We present a "Branch & Fix" type algorithm that solves the HCP (and in the process the above global optimisation problem for Hamiltonian graphs). At each branch of the algorithm, only a linear program needs to be solved and the dimensions of the successive linear programs are shrinking rather than expanding. Another optimization problem is that of minimizing the variance of first return times to the home node. The latter, in turn, leads to an interesting problem of minimizing the determinant of a rank-one corrected generator of a Markov chain. All of these formulations lead to some challenging, still unsolved, problems.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Wadim Zudilin, The University of Newcastle
• Topic: Hankel Determinants and More Than Irrationality
• Location: Room V205, Mathematics Building,
  The University of Newcastle
• Date and Time: February 10^th, 2010 (Wednesday), 2:30 pm

• CARMA COLLOQUIUM
• Speaker: Laureate Professor Jonathan Borwein, The University of Newcastle
• Topic: Douglas-Ratchford Iterations in the Absence of Convexity
• Coauthor: Brailey Sims, University of Newcastle
• Location: Room V129, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: January 28^th, 2010 (Thursday), 4:00 pm
• Abstract:

  The Douglas-Rachford iteration scheme, introduced half a century ago in connection with nonlinear heat flow problems, aims to find a point common to two or more closed constraint sets.

  Convergence of the scheme is ensured when the sets are convex subsets of a Hilbert space, however, despite the absence of satisfactory theoretical justification, the scheme has been routinely used to successfully solve a diversity of practical problems in which one or more of the constraints involved is non-convex. As a first step toward addressing this deficiency, we provide convergence results for a proto-typical non-convex scenario.

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Jonathan Borwein, The University of Newcastle
• Topic: PSLQ and its Applications II
• Location: Room V205, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time: January 20^th, 2010 (Wednesday), 2:30 pm

• CARMA ANALYSIS and NUMBER THEORY SEMINAR
• Speaker: Jonathan Borwein, The University of Newcastle
• Topic: PSLQ and its Applications
• Location: Room V205, Mathematics V, Callaghan Campus,
  The University of Newcastle
• Date and Time:November 25^th, 2009 (Wednesday), 2:30p.m.

• CARMA Seminar
• Speaker: Laureate Professor Jon Borwein, The University of Newcastle
• Title: Compressed Sensing: a Subgradient Descent Method for Missing Data Problems
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: November 19^th, 2009 (Thursday), 4:00 pm
• Abstract: This is joint work with Russell Luke (Heidelberg and Delaware)

• CARMA Seminar
• Speaker: James Wan, PhD Student, CARMA, The University of Newcastle
• Title: Random Walk Integrals
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: November 12^th, 2009 (Thursday), 4:00 pm
• Abstract: In this talk, I will consider a family of n-dimensional integrals arising from the theory of random walks (as well as other origins going back to Lord Rayleigh). I will attempt to uncover some of the problem's fascinating structure via unexpected conspiracy and interplay among combinatorics, analysis (complex and numerical) and probability. I will present some interesting original results in this joint work with Borwein, Nuyens and Straub. Free open problems will also be provided.

• CARMA Seminar
• Speaker: Associate Professor Brailey Sims, University of Newcastle
• Title: Fixed Point Theory in Metric Spaces
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: November 5^th, 2009 (Thursday), 4:00 pm
• Abstract: In my previous talk I surveyed the development of metric fixed point theory (the theory of fixed points for nonexpansive maps) in Banach spaces from its inception to the present, exposing its rich and symbiotic interplay with the geometry of the space. In this talk I will examine the extension into metric spaces. Such extensions are significant as they provide a theory in contexts where no natural linear structure is present; for example, state spaces and certain models of cognition. Our focus will be on conditions under which every nonexpansive mapping T:X → X of a metric space (X.d) into itself has a fixed point. Recall T is nonexpansive if, d(Tx, Ty) ≤ d(x, y) for all x, y in X. We will trace developments from their beginnings in the late 1970’s to the exciting currently emerging theory in geodesic metric spaces of negative and positive curvature (in the sense of Gromov), in particular in the so called CAT(0) spaces.

• Official CARMA Opening and Conference
• Speakers include:
  • Richard Brent (ANU)
  • Tony Guttmann (Melbourne)
  • Warren Moors (Auckland)
  • Andrew Eberhard (RMIT)
  • Jerry Joseph (IBM, Canberra)
• Program: Download Program (pdf)
  
  • Conference Photos (Coming Soon)
  • Conference Presentations
  • A John Giles Sampler (Coming Soon)
• Registration Form: Download Registration Form (pdf)
  Abstracts:Download Abstracts (pdf)
  Organizer: Jonathan Borwein
• Location: CARMA Centre, Mathematics V, Callaghan Campus, University of Newcastle
• Date: October 30^th to November 1^st, 2009.

• CARMA Seminar
• Speaker: Matteo Fischetti, DEI, University of Padova, Italy
• Title: Just MIP it!
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: October 29^th, 2009 (Thursday), 4:00 pm
• Abstract: Modern Mixed-Integer Programming (MIP) solvers exploit a rich arsenal of tools to attack hard problems. It is widely accepted by the OR community that the solution of very hard MIPs can take advantage from the solution of a series of time-consuming auxiliary Linear Programs (LPs) intended to enhance the performance of the overall MIP solver. E.g., auxiliary LPs may be solved to generate powerful disjunctive cuts, or to implement a strong branching policy. Also well established is the fact that finding good-quality heuristic MIP solutions often requires a computing time that is just comparable to that needed to solve its LP relaxation. So, it makes sense to think of a new generation of MIP solvers where auxiliary MIPs (as opposed to LPs) are heuristically solved on the fly, with the aim of bringing the MIP technology under the chest of the MIP solver itself. This leads to the idea of "translating into a MIP model" (MIPping) some crucial decisions to be taken within a MIP algorithm (How to cut? How to improve the incumbent solution? Is the current node dominated?). In this paper we survey some successful applications of the above approach.

• CARMA Seminar
• Speaker: Joydeep Dutta, Indian Institute of Technology, Kanpur
• Title: Is Bilevel Programming a Special Case of Mathematical Programming Problems with Complementarity Constraints?
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: October 22^nd, 2009 (Thursday), 4:00 pm
• Abstract: The answer to the question is of course "NO" when the lower-level problem is non-convex but it is surprising to see that the answer is still "NO" when the lower-level problem is a convex or even a linear one. We show that under strong conditions both the bilevel problem and the MPCC problem are closely related and the solution of one of the problem is also the solution of the other. We demonstrate through simple examples that without these strong conditions in general the bilevel programming problem and the MPCC problem cannot be related through their solutions, local or global.

• CARMA Seminar
• Speaker: Brailey Sims, University of Newcastle
• Title: Metric fixed point theory - past, present and future
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: October 8^th, 2009 (Thursday), 4:00 pm
• Abstract: Can be found here (MS Word document)

• CARMA Seminar
• Speaker: Joydeep Dutta, Indian Institute of Technology-Kanpur, India
• Title: Gap Functions and Error Bounds for Vector Variational Inequalities
• Location: Room V206 - Access Grid Room via University of South Australia
• Date and Time: September 18^th, 2009 (Friday), 2:30 p.m.
• Abstract: Vector variational inequalities are motivated from the necessary optimality conditions for smooth vector optimization problems over convex sets. There are several types of vector variational inequalities but in this talk we concentrate on the Stampacchia type weak vector variational inequality. Our main aim is to devise some scalar valued gap functions which lead to constrained and unconstrained reformulations of the vector variational inequality problem. We also use these gap functions to devise error bounds for the Stampacchia type weak vector variational inequality problem.

• CARMA Seminar
• Speaker: Professor Mirka Miller, School of Electrical Engineering and Computer Science, University of Newcastle
• Title: Recent advances in the degree/diameter problem
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: September 17^th, 2009 (Thursday), 4:00 p.m.
• Abstract: The (undirected) degree/diameter problem is to find the maximum possible number of vertices in a graph with given diameter and maximum degree. The corresponding problem for directed graphs uses maximum out-degree instead of maximum degree. In this talk we will give an overview of the progress of the degree/diameter problem for both directed and undirected graphs, and a number of related open problems.

• CARMA Seminar
• Speaker: Professor Natashia Boland, University of Newcastle
• Title: A multistage stochastic integer programming approach to long term mine scheduling
• Organizer: Jonathan Borwein
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: September 10^th, 2009 (Thursday), 4:00 p.m.
• Abstract: The Open Pit Mine Production Scheduling Problem is usually based on a single geological estimate of material to be excavated and processed. While some attempts have been made to use multiple stochastic geological estimates in mine production scheduling, none allow mining and processing decisions to flexibly adapt over time, in response to observation of the geology of the material mined. We present a mixed integer multistage stochastic programming approach and discuss a number of reductions that can be used to lower the computational effort of solving this model. We also discuss heuristics that can be used to further reduce solution times and illustrate the various numerical approaches on realistic data sets.

• CARMA Seminar
• Speaker: O-Yeat Chan, University of Newcastle
• Title: Divisibility properties of Stirling numbers of the second kind
• Organizer: Jonathan Borwein
• Location: Room V129, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: September 3^rd, 2009 (Thursday), 4:00 p.m.
• Abstract: The Stirling numbers of the second kind S(n,k) count the number of ways to partition a set of size n into exactly k non-empty subsets. These numbers arise often in combinatorics and are closely related to other number sequences such as the Bell numbers. Inspired by some recent results of Amdeberham, Moll, and Manna on the 2-adic valuations of S(n,k) for fixed k, we studied the behaviour of S(n,k) mod p^m for general primes p. We will discuss some of our methods and results in this talk.
  
  This is joint work with Dante Manna at Virginia Wesleyan College.

• CARMA Seminar
• Speaker: Professor Paul Manuel (University of Kuwait)
• Title: "History of Computer Science (A Journey from Mathematics to Computer Science)"
• Organizer: Jonathan Borwein
• Location: CARMA Centre, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: August 27^th, 2009 (Thursday), 4:00 p.m.
• Abstract: Historians debate whether the history of computer science starts from the abacus invented in Babylon in 2400 BC or from the Analytical Engine developed by Charles Babbage in 1837. In this seminar we look into historical developments of computer science ignited by David Hilbert since 1920 and ending with Cook's NP completeness. The talk finishes with the open problem of the 20th century.

Three CARMA Seminars: August 20^th, 2009:

• CARMA ANALYSIS SEMINAR and SIGMAOPT DISTRIBUTED SEMINAR
• Speaker: Jonathan Borwein, University of Newcastle
• Title: "Hilbert Inequalities and Witten Zeta-functions"
• Location: CARMA V205, Mathematics V, Callaghan Campus,
  University of Newcastle
• Date and Time:August 20^th, 2009 (Thursday), 2:30p.m.
• Abstract: Inequalities are central to optimization and most other branches of mathematics:

  Harald Bohr is reported to have remarked "Most analysts spend half their time hunting through the literature for inequalities they want to use, but cannot prove." (D.J.H. Garling)

  In this talk I shall describe some wonderful classical inequalities as well as some modern consequences and connections.

• CARMA Seminar
• Speaker:Professor Dominique Buset (Université Libre de Bruxelles, Belgium)
• Title:"The Degree/Diameter Problem: 45 Years of Progress"
• Organizer: Jonathan Borwein
• Location: Rm.V206, Mathematics V, Callaghan Campus, University of Newcastle
• Date and Time: August 20^th, 2009 (Thursday), 12:00 noon
• Abstract: During the sixties, with the extension of interconnection networks, engineers had been confronted by problems which turn out to be related to graph theory. One of them was proposed in 1964 by Elspas: Given two integers D and D, construct a simple connected graph with maximum degree D, diameter D and with maximum possible number of vertices. Moreover, another question immediately followed: What is the maximum number of vertices of such a graph? Many mathematicians, engineers and computer scientists have been working on these two problems. The purpose of this talk is to give an overview about the state-of-art of this problem and to tackle the determination of the exact value of the maximum number of vertices of a connected undirected (D,D)-graph.

• CARMA Seminar
• Speaker: Professor Donald Cartwright (University of Sydney)
• Title: "Enumeration of the 50 Fake Projective Planes"
• Organizer: Jonathan Borwein
• Location: Rm. V129, Mathematics V, Callaghan Campus,
  University of Newcastle
• Date and Time: August 20^th, 2009 (Thursday), 4:00 p.m.
• Abstract: This is joint work with Tim Steger. Fake projective planes are smooth compact complex surfaces which are not the complex projective plane, but have the same Betti numbers as the complex projective plane. It was known that there are only finitely many of them, and they are determined by their fundamental group.In their 2007 Inventiones paper, Gopal Prasad and Sai-Kee Yeung showed that these fundamental groups are the torsion free subgroups Pi, with finite abelianization, of a certain index in certain maximal arithmetic subgroups G of PU(2,1). They show that only a small number of G's can arise, and list them explicitly. Using computers heavily, Tim Steger and I have now found all the possible groups Pi for all of these G's, by finding explicit generators and relations for each of these groups G. Thus all fake projective planes have now been found. I shall report on some aspects of this work. (Note: this talk is largely complementary to the earlier talk by Tim Steger.)

• CARMA Workshop on Multidimensional Numerical Integration
  and Special Function Evaluation
• Speakers include: David Bailey (LBNL) and Ian Sloan (UNSW)
• Organizer: Jonathan Borwein
• Location: Rm. V206 - Access Grid Room -, Mathematics V, Callaghan Campus,
  University of Newcastle
• Date: August 18^th, 2009 (Tuesday).