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