FSCIT RESEARCH BROCHURE - PAGE 1

COMPUTER ASSISTED RESEARCH MATHEMATICS and its APPLICATIONS
(CARMA)

Newcastle Access Grid Room / OVERVIEW
Two decades ago, relatively few mathematicians employed computations in serious research work. In fact, there appeared to be a wide-spread view in the field that “real mathematicians don'tcompute.'' In the ensuing years, computer hardware has skyrocketed in powerand plummeted in cost, thanks to the remarkable persistent phenomenon of Moore's Law. In addition, numerous powerful mathematicalsoftware products, both commercial and non-commercial, have become available. But just as importantly, a new generation ofmathematicians is eager to use these tools.Consequentlynumerous new results are being discovered, and the use of mathematics in business and industry is expanding rapidly.
An experimental methodology provides a compelling way to build insight,to generate and confirm or confront conjectures; and generally to make mathematics more tangible, lively and fun for theprofessional researcher, for the practitioner and for the novice.
Advanced mathematical computation is equally essential to the solution of real-world problems; much sophisticated mathematics is core tothe software used by the engineers, scientists, managers and decision-makers who design, plan and control the products and systemscentral topresent day life. / OBJECTIVES
►To perform research and development relating to the informed use of computers as an adjunct to mathematical discovery (including current advances in cognitive science, in information technology, operations research and theoretical computer science)
►To perform research and development of mathematics underlying computer-based decision support systems, particularly in automation and optimization of scheduling, planning and design activities, and to undertake mathematical modelling of such activities
►To promote and advise on the use of appropriate tools (hardware, software, databases, learning object repositories, mathematical knowledge management, collaborative technology) in academia, education and industry
►To make University of Newcastle a world-leading institution for COMPUTER ASSISTED RESEARCH MATHEMATICS and itsAPPLICATIONS /
EXTERNAL COLLABORATORS
(current and recent) BHP Billiton; Constraint Technologies International Pty Ltd; Canadian National Centre of Excellence for Mathematics of Information Technology and Complex Systems; CSIRO Energy Technology; Mater Hospital, Radiation Oncology Department; Hunter New England Area Health, Service, Innovation and Reform Unit; Hunter Valley Coal Chain Logistics Team; MapleSoft Inc; Mathematical Association of America; International Mathematical Union; MathResources Inc; National Institute of Standards and Technology; Sun Micro Systems.
RESEARCH SUPPORT
ARC and NSERC discovery grants, ARC Linkage International grants,
ARC linkage grants with BHP-Billiton, CTI Pty Ltd; NIST, Volkswagen Foundation.
Student/RA support from DSTO MOD, International Mathematical Union.
MapleSoft, MathResources, and Sun Microsystems.

FCSIT RESEARCH BROCHURE - PAGE 2

The MountainPass and
a Highly Nonlinear Problem / EXAMPLES OF CURRENT PROJECTS
AnalysisClassical,harmonic, non-linear and convex analysis. Fixed point theory for non-reflexive Banach spaces.
Simple Topological GroupsTowards a classification of simple totally disconnected locally compact groups.
Continuous OptimizationMaximum entropy optimization, wavelet analysis and image reconstruction methods
Discrete OptimizationScheduling algorithms for open-pit mining, accurately solving and to model the effects of uncertainty in geological estimates on the extraction schedule.
RESEARCH OUTCOMES
Current best results on irrationality of Zeta-function values obtained.
Leading edge results on structure of maximal monotone operators.
Lower cost airline schedules thatare more robust to operational disruptions.
Design of pill fabrication for major international drug company.
Optimized delivery of radiotherapy (IMRT) treatment for cancer.
Largest accurate geological models for mineral extraction. / GROUP MEMBERS
Dr Brian Alspach; Dr Ian Benn; Professor Natashia Boland; Laureate Professor Jonathan Borwein; Dr Jeffrey Hogan; Dr James MacDougall; A/Professor Brailey Sims; A/Professor George Willis; Dr Xin-She Yang; A/Professor Wadim Zudilin
RESEARCH TOPICS
Topological Groupsincluding: structure of totally disconnected groups and their automorphisms; links with harmonic analysis, geometry, number theory and discrete mathematics.
Linear and Nonlinear Analysisincluding:Convexity; Variational methods; Metric fixed point theory; Banach space geometry; Frames and wavelet analysis. Applicationsto evolving systems, control, optimization, and image and signal reconstruction.
Computational Analysis and Number Theory Computer assisted study of links between number theory, knot theory and mathematical physics.Development of mathematical data-mining tools.
Optimization and Simulation Techniques: better models and algorithmsfor mathematicaloptimization and solution of large-scaleproblems, including integration withconstraint programming and meta-heuristic techniques.
Study of Non-porous Mediainvolves coupled systems of partial differential equations with applications to geotectonics and pattern formation. /
CONTACT
Group Facilitator Laureate Professor Jonathan Borwein
School of Mathematical and Physical Sciences
University of Newcastle
Callaghan NSW 2308 Australia
Phone: +61 2 49215440
Email:
Website:

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