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.
Structure and auto-morphisms of totally disconnected groups; links to
harmonic analysis, geometry, number theory and discrete maths.
Fourier analysis, wavelets, time-frequency analysis, sampling and
signal processing applications; singular integrals and frames; Clifford
analysis and applications to hypercomplex signal processing.
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.
Classical, harmonic, non-linear, convex analysis. Fixed point theory
and variational analysis in nonreflexive space.
Maximum entropy optimization, wavelet analysis and image reconstruction
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
- 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.
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