 CARMA COLLOQUIUM
 Speaker: Dr Judyanne 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
2dimensional 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: HighPrecision 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 64bit floatingpoint 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 highprecision software packages that
include highlevel 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 nbody 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 highprecision arithmetic facilities are now an indispensable component of a modern largescale
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 AtkinHecke 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 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 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 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 middleaged 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: OYeat 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 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 nonpositive curvature, called CAT(0)
spaces. These include complete simply connected Riemannian manifolds of nonpositive sectional curvature,
Rtrees, 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 thirtytwo 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 timelike
linear ordering of ideals that is seen in 1parameter convolution algebras.

 CARMA ANALYSIS and NUMBER THEORY SEMINAR
 Speaker: OYeat 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
 Cosponsored 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 socalled "conditional
valueatrisk," 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: Leastsquares 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 qrious 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: HighResolution 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.
Highresolution shockcapturing 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 NonConvex 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
stateaction 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 rankone 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: DouglasRatchford 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 DouglasRachford 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 nonconvex. As a first step toward addressing this deficiency, we provide convergence results for a prototypical nonconvex 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 ndimensional 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.



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 MixedInteger 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 timeconsuming 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 goodquality
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
lowerlevel problem is nonconvex but it is surprising to see that the answer is still "NO"
when the lowerlevel 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 TechnologyKanpur, 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 outdegree 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: OYeat 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 nonempty 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 2adic 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 Zetafunctions"
 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 stateofart 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
SaiKee 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 Seminar
 Speaker: Anne Thomas, Cornell University
 Title: "Existence, Covolumes and Infinite Generation of Lattices for Davis Complexes"
 Organizer: Jonathan Borwein
 Location: Rm. V129, Mathematics V, Callaghan Campus,
University of Newcastle
 Date and Time: August 14^{th}, 2009 (Friday), 2:00p.m.
 Abstract:
Let Sigma be the Davis complex for a Coxeter system (W,S). The automorphism group G of Sigma is naturally
a locally compact group, and a simple combinatorial condition due to HaglundPaulin determines when G is nondiscrete. The Coxeter group W
may be regarded as a uniform lattice in G. We show that many such G also admit a nonuniform lattice Gamma, and an infinite family of
uniform lattices withcovolumes converging to that of Gamma. We also show that the nonuniform lattice Gamma is not finitely generated.

 CARMA Colloquium and SIGMAopt Distributed Seminar
 Speaker: David H. Bailey, Lawrence Berkeley National Laboratory
 Title: "Computing: The Third Mode of Scientific Discovery"
[Talk in PDF]
 Organizer: Jonathan Borwein
 Location: Rm. CARMA V205, Mathematics V, Callaghan Campus,
University of Newcastle
 Date and Time: August 13^{th}, 2009 (Wednesday), 2:30p.m.3:30p.m.
 Abstract:Scientific computation has come a long way in the 50 years since the first production computers
became available. The latest stateoftheart systems have achieved over 1 "petaflops", or in other words, over 1 quadrillion
(10 to the fifteenth power, or one million billion) floatingpoint arithmetic operations per second.
[Full Abstract]

 Weekly CARMA Colloquium
 Speaker: Dr. Jason Harris, PhD (Canterbury), BSc (Hons) Otago, BSc (Hons) Canterbury, Wolfram Research as a member of the core development team for Mathematica.
 Title: The New Era of Mathematica Technology
 Organizer: Jonathan Borwein
 Location: Rm. V107, Mathematics V, Callaghan Campus,
University of Newcastle
 Date and Time: August 6^{th}, 2009 (Thursday) from 4:00p.m.5:00p.m.
[followed by wine and cheese].

 Weekly CARMA Colloquium
 Speaker: Professor Tim Steger, Department of Mathematics and Physics,
Università degli Studi di Sassari, Italy.
 Organizer: Jonathan Borwein
 Location: Rm. 129, Mathematics V, Callaghan Campus,
University of Newcastle
 Date and Time: July 30^{th}, 2009 (Thursday) from 4:00p.m.5:00p.m.


