With over 33 mathematicians and eight statisticians, the Department of Mathematics and Statistics has members pursuing active research programs in both the traditional and more modern areas of mathematics, pure and applied, in statistics and in probability. More specifically, in mathematics, our strengths include algebra, analysis, combinatorics, geometry and algebraic topology. Within the broad spectrum of applied mathematics, we have particular expertise in the numerical analysis of Volterra and integro-differential equations, theoretical space physics, ship hydrodynamics, computer modelling and mathematical control theory.
In statistics, our interests range from mathematical to applied. A statistical consulting service, which the department provides to the university community, brings a wide assortment of fascinating applied problems to our attention.
BOOTH, Peter I. Professor
Keywords
• Topology
Current research
• Homotopy theory
Past research
• Topology of function spaces
• Category theory and categorical topology
• Applied catastrophe theory
BRUNNER, Hermann Research professor
Keywords
• Numerical analysis of Volterra; integral and functional
differential equations; collocation methods for weakly singular
Volterra integral and integro-differential equations
Current research
• Collocation for delay differential and integral equations
with proportional delays
• Numerical solution of neutral functional, integro-differential
equations with weakly singular kernels
Past research
• Numerical analysis of nonlinear and delay Volterra integral
equations
Potential research
• Numerical analysis of nonlinear integral and integro-differential
equations with slow-up solutions
BURRY, John Professor
Keywords
• Measure-information theory
Current research
• Fractal and chaos
• Fractal image compression
• Mathematics of finance and Chaos Theory
Past research
• Measure theory
EDDY, Roland H. Professor
Keywords
• Affine and projective geometry; cremona; simplexes; transformations;
Skew-orthologic
Current research
• Cremona transformations
• Associated simplexes
• Specialized coordinate systems
Past research
• Triangle inequalities
FOSTER, Andy Associate professor
Keywords
• Dyanamical systems; bifurcation; chaos; mathematical modeling;
mathematical biology
Current research
• Deterministic mathematical models in population biology
• Dynamical systems approach to numerical solutions for differential
equations
• Chaotic saddles in discrete dynamical systems
Past research
• Bifurcation sequences in dynamical systems
• Prediction of tertiary structures of proteins
• Linear optimization approach to geometric inequalities
Potential research
• Mathematical modeling in physiology
GASKILL, Herbert Professor
Keywords
• Modeling; simulation
Current research
• Gravitational dynamics of star clusters; n-body problems
Past research
• Industrial applications of mathematics
Special equipment or facilities
• 50-node Beowulf cluster
GOODAIRE, Edgar G. Professor
Keywords
• Algebra
Current research
• Moufang loops
• Alternative rings
• Loop rings
• Unit loops of loop rings
Past research
• Alternative loop rings
• Alternative rings of small order and dimension
• Nilpotent right alternative rings, commutative alternative
rings
Potential research
• Subloops of Zorn's matrices
• Right alternative loop rings, and their units
• Loops with unique nonidentity commutators
• Symmetric units in loop rings
• Ring flexible loops
GRANT McLOUGHLIN, John (See Education)
KOCABIYIK, Serpil Associate professor
Keywords
• Computational and theoretical fluid dynamics; Asymptotics
and perturbation methods; scientific computation
Current research
• Unsteady viscous flows around cylindrical structures
• Partial differential equations, numerical solutions
• Flow-induced vibrations
Past research
• Analysis of low Reynolds number flows
Potential research
• Heat transfer
• Optimum design
LEE, Chu-In Charles Professor
Keywords
• Isotonic regression; stochastic ordering; multiple comparison;
dose response problem; simultaneous confidence interval;
nonparametric statistical inference
Current research
• Goodness-of-fit test for uniform stochastic ordering among
several populations
• Nonparametric estimation of bonded survival functions,
with censored observations
• Chi-squared tests for and against stochastic ordering on
multinomial parameters
Past research
• Monotone dose-response curve, estimation
• Multinomial estimation procedures for two stochastically
ordered distributions
• Rank transformed regression, consistency
Potential research
• A multiple-comparisons procedure for detecting differences
between treatments, a control in two-factor experiments
• A one-sided, multiple comparison procedure, restricted
normal models
• Simultaneous confidence bounds for monotone regression
curves
LI, Yuanlin Assistant professor
Keywords
• Nilpotent groups; metabelian groups; grouprings; units;
normalizer; Zassenhaus conjectures; modules; homological dimensions;
K-theory; Whitehead group
Research specialty
• The group ring of a group $G$ over a commutative ring $K$,
the ring $KG$ of all formal finite sums: $\alpha = \sum_gg$, applications
in coding theory
Current research interest
• Group rings: units and related topics
• Homolagical properties of rings
• Algebraic K-theory
Past research
• Group rings: units and related topics
• Homolagical properties of rings
• Algebraic K-theory
Potential research
• Lie algebra
• Incidence algebra
MAY, Sherry Director, Mathematics Learning Centre
Keywords
• Modelling; Automaticity; Remedial mathematics software
Current research
• Modelling to estimate the effects of income security reform
• Effect of prerequisite skills on performance in post-secondary
mathematics courses
• Development of mathematics software for remediation
Past research
• An economic model of household production (Royal Commission
on Employment and Unemployment)
• Development of a pest management system for the eastern
hemlock looper
• Perception and cognition testing for the mentally handicapped
NARAYANASWAMI, Pallasena P. Professor
Keywords
• Functional analysis; locally convex spaces; barrelled;
bornological; nuclear; Frechet spaces
Current research
• Structure theory of Frechet and (LF)-spaces
• Problems in barrelled, nuclear and Baire-like spaces
• The separable quotient problem in Banach spaces
Past research
• Open mapping and closed, graph theorems in locally, convex
spaces
• (LF)-spaces, (db)-spaces and the separable quotient problem
• Classification of (LF)-spaces; quasi-Baire spaces; the
strongest locally convex topology on a countable-dimensional linear
space
Potential research
• Search for dense, non-barrelled subspaces
• Locally convex spaces generated by a closed graph, or an
open-mapping theorem
• Problems in infinite, dimensional holomorphy
OYET, Alwell J Assistant professor
Keywords
• Robust minimax designs for estimation; extrapolation of
nonparametric regression models based on wavelet approximations;
bilinear time series modelling
Current research
• Integer-valued, wavelet minimax designs for nonparametric
models
• Comparison of nonlinear curves, wavelet regression
Past research
• Wavelet designs for estimating nonparametric curves
• Heteroscedastic error
• Nonlinear, time series modelling: pattern recognition and
wavelet
• Filtering
Potential research
• Extrapolation designs for nonparametric models based on
wavelet representations
• Wavelet designs for nonparametric models, infinitesimal
approach
PARMENTER, Michael Professor
Keywords
• Ring theory; group theory; Actuarial mathematics
Current research
• Group rings; incidence algebras; normalizing extensions
Past research
• Covering systems of cosets
Potential research
• Graph theory
PENG, Yingwei Assistant professor
Keywords
• Biostatistics; medical statistics; statistical computing;
data analysis; multivariate analysis
Current research
• Survival analysis
• Generalized linear models
• Statistical software for cancer, clinical studies
Past research
• Clustering analysis
• Quality control and statistics
• Database management
Potential research
• Statistical genetics
• Clinical trial design and study
• Epidemology
PIKE, David A. Assistant professor
Keywords
• Combinatorics, discrete math, graph theory
Current research
• Graph decompositions
• Cycle properties of graphs
REES, Rolf Associate professor
Keywords
• Combinatorial design theory; graph decompositions; external
graph theory
Current research
• Mandatory representation designs
• Constructions for new classes of group-divisible designs
• Maximal sets of r-factors in complete graphs
Past research
• Perfect pair-coverings and restricted resolvable partitions
• Embeddings of designs
• Development of new constructions for resolvable group-divisible
designs
Potential research
• Packing and covering arrays
• Applications of combinatorial designs, cryptography
SABIN, Gary (See Engineering)
SHAWYER, Bruce L.R. Professor
Keywords
• Approximation theory; summability; integrals; LaTeX macros
Research specialty
• Acceleration of convergence of slowly convergent series
• Efficient macros for the drawing of diagrams in LaTeX
Current research
• Automatic scaling of diagrams in LaTeX
• Automatic font selection of diagrams in LaTeX
Past research
• Acceleration of convergence of slowly convergent series
SINGH, Santkatha Professor
Keywords
• Fixed point theory; best approximation; equilibrium point;
KKM-map principle; Variational inequalities; minimax theory; maximal
element
Research specialty
• Non-linear functional analysis; approximation theory; variational
inequalities; maximal elements in economics
Current research
• Best approximation and applications
• Variational inequalities
• Fixed-point theory and applications
Past research
• Nonexpansive mappings and fixed points
• Fixed-point theory and its applications, approximation
theory
• Applications of fixed-point theory, economics
Potential research
• Maximal elements in ecomonics
• Nonlinear problems in functional analysis
• Complementarity theory and variational inequalities
SNEDDON, Gary Assistant professor
Keywords
• Regression; time series; geostatistics; mixture modelling;
underdetermined models; Bayesian statistics
Current research
• Bayesian approach to ensemble forecasting in weather predictions
• Statistical perspective on data assimilation
• Robust estimation in undetermined regression models
Past research
• Smoothing in undetermined regression models
• Bayesian analysis of a precipitation model
Potential research
• Estimation in undetermined regression models with correlated
errors
• Variance component estimation in semi-parametric models
SUMMERS, Danny Professor
Keywords
• Space physics; plasmas; plasma waves; nonlinear dynamics;
chaos; magnetospheres; applied mathematics
Research specialty
• Theoretical space physics
• Plasma dynamics
• Nonlinear dynamics and chaos
Current research
• Magnetospheric processes
• Wave-particle interactions and instabilities in plasmas
• Nonlinear dynamical systems in the sciences
Past research
• Solar wind theory
• Reachability and controllability in control systems
• Chemical reaction kinetics
Potential research
• Further research in theoretical space physics
• Further research in plasma theory
• Further research in nonlinear systems in the sciences
SUTRADHAR, Brejendra C. Professor
Keywords
• Correlated data; diserete or continuous; robust inference;
elliptical distribution; time series; sampling; data analysis
Current research
• Analyzing longitudinal data subject to non-response
• Nonlinear regression analysis
• Biostatistics
• Time series, valued experimental design, with applications
for socioeconomics
Past research
• Estimation of parameter of a regression model with terror
variable
• Variance estimation for systematic sampling
• Time series, valued experimental designs, one-way classification
Potential research
• Robustness in multivariate analysis
• Design of experiments with ARMA error structure
• Correlated data analysis
WANG, Hong Associate professor
Keywords
• Large order statistics; zero-one laws; stability theorems;
multi-parameter random fields; local time; level sets; Hausdorff
Dimension; sojourns of a stochastic process; Martingle;
Markov processes
Current research
• Extreme value theory of large order statistics for non-i.i.d.
random variables
• Extreme values generated by Markov processes
• Gear selectivities and survival rate on fishing experiments
Past research
• Extreme value theory of large order statistics for i.i.d.
random variables
• Markov processes and Martingale theory for multi-parameter
time index
• Random fields and their geometry
Potential research
• Martingale applications in extreme value theory
• Stable laws for the sojourns of a diffusion process
• Application of external trunked data
WANG, Xikui (See Medicine)
WATSON, Bruce Professor
Keywords
• Analysis
Current research
• Tauberian theorems in summability theory
• Results in fixed-point theory
Past research
• Summability theory
• Fixed-point theory
Potential research
• Application of integral transforms in summability theory
• Results in fixed-point theory
ZHAO, Xiaoqiang Assistant professor
Keywords
• Applied mathematics; nonlinear differential equations;
applied dynamical systems; mathematical biology
Current research
• Dynamics of a periodically pulsed, bio-reactor model
• Persistence and extinction in two species, reaction-diffusion
systems with delays
• Microbial growth in a plug flow reactor with wall adherence
and cell motility
Past research (selected)
• Uniform persistence and periodic coexitence states in infinite
dimensional periodic semiflows, with applications
• Global asymptotics in quasimonotone, reaction-diffusion
systems with delay
• N-species competition in a periodic chemostat
Potential research
• Global asymptotic stability of traveling waves in delayed-reaction
diffusion equations
• Chain transitivity, attractivity and strong repellors for
semidynamical systems
• A non-local delayed and diffusive predator-prey model
ZHOU, Yiquang Assistant professor
Keywords
• Associative pings and Module theory
Current research
• Natural classes of modules and type theory of modules
• Sublattice structure of the lattice pre-natural classes
of modules
• Injectivity of modules and annihilator conditions of rings
Past research
• Module classes
• Finiteness conditions of rings and modules
• Radical theory
Potential research
• Module theory over group rings
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