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.

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.

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.

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.

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.