[The University of Newcastle, Australia]
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Priority Research Centre for Computer-Assisted
Research Mathematics and its Applications



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Summer Holiday Research Topics

Details of research topics for summer scholarships are available here.
For details of the research infrastructure available at CARMA, please visit our equipment web page.

Research
Topics

Computational Analysis and Number Theory

Computer-assisted study of links between analysis, number theory, knot theory and mathematical physics. Development of mathematical data-mining tools. Discrete Mathematics: all aspects of graph theory with emphasis on algebraic graph theory and ties to design theory.

Linear and Nonlinear Analysis

Convexity; variational methods; fixed point theory; Banach space geometry; frames and wavelet analysis. Applications to dynamical systems, control, optimization, and image or signal reconstruction.

Optimization and Simulation

Models and algorithms for optimization and solution of large-scale problems, using constraint programming and metaheuristics. Study of Non-porous Media with coupled systems of partial differential equations applied to geotectonics and pattern formation.

Topological Groups

Structure and auto-morphisms of totally disconnected groups; links to harmonic analysis, geometry, number theory and discrete maths.

Harmonic Analysis

Fourier analysis, wavelets, time-frequency analysis, sampling and signal processing applications; singular integrals and frames; Clifford analysis and applications to hypercomplex signal processing.

Number Theory

Arithmetic, algebraic and combinatorial properties of solutions of differential and difference equations; (in)dependence of numbers that come as values of special functions; Diophantine analysis.
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EXAMPLES OF
CURRENT PROJECTS

Analysis

Classical, harmonic, non-linear, convex analysis. Fixed point theory and variational analysis in nonreflexive space.

Continuous Optimization

Maximum entropy optimization, wavelet analysis and image reconstruction methods.

Discrete Optimization

Accurate scheduling for open-pit mining, modelling effects of uncertainty in geological estimates on the extraction schedule. Simple Topological Groups Understanding simple totally disconnected locally compact groups.
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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 that are 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.
  • Consultation with gaming industry, real-world network design and scheduling.
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RESEARCH
SUPPORT

ARC and NSERC Discovery grants, ARC Linkage International grants, ARC Linkage grants with BHP-Billiton, CTI Pty Ltd; MITACS, NIST, and Volkswagen Foundation. Student/Research Assistant support from DSTO MOD, International Mathematical Union, MapleSoft, MathResources, and Sun Microsystems.
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EXTERNAL
COLLABORATORS

BHP Billiton; Constraint Technologies International Pty Ltd; Canadian National Centre of Excellence for Mathematics of Information Technology and Complex Systems (MITACS); 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.
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