The research interests of our faculty members fall into five broad categories:

Algebra and Logic (Andrew P. Dean, Greg Lee)

Analysis (Razvan Anisca, Yin Chen, Andrew J. Dean, Monica Ilie, Liping Liu, Tianxuan Miao, and Maria Grazia Viola)

Applied Mathematics/PDE (Liping Liu)

Optimization/Operations Research (Wendy Huang and Liping Liu)

Probability and Statistics (Wendy Huang and Deli Li)
Algebra
Greg Lee is interested in noncommutative algebra, with an emphasis on group rings. He has a particular interest in the Lie structure of the group ring, as well as the structure of its unit group. He is also interested in the theory of group representations.
Analysis
Razvan Anisca's research is mainly in Geometric Functional Analysis, which is the study of finite and infinite dimensional Banach spaces. An important part of his research is focussed on the structural properties of infinite dimensional Banach spaces, that is, the
behaviour of their subspaces. The phenomena investigated are infinite dimensional in nature, or they may depend on the asymptotic
behaviour of certain finite dimensional invariants. As such, the finite dimensional theory (local theory) of Banach spaces makes an importantcontribution to the understanding of the geometry of infinite dimensional Banach spaces.
Yin Chen's primary interest is in analytic multifunctions and their applications in spectral theory. Some of the problems he is investigating are: (a) It is known that under a certain condition, the spectrum of a closed interpolated operator is an analytic multifunction. Is this condition necessary? When is the spectrum constant? (b) Find the optimal estimate for the Hausdorff distance between the spectra of two algebraic elements of a Banach algebra. (c) Study the implications between the power boundedness and some resolvent conditions for Banach space operators. Find the best possible constants related to these implications. (d) Study the analytic multifunctions on the disk. Extend some wellknown inequalities for analytic functions and harmonic functions to analytic multifunctions and then find applications back in classical complex analysis.
Andrew J. Dean's research deals with C*dynamical systems, in particular, constructing invariants to classify categories of them. He is also interested in graph C* algebras and real structures on C* algebras.
Monica Ilie's research lies in the area of abstract harmonic analysis, with an emphasis on its interplay with operator space theory. Operator space theory is sometimes referred to as "quantized" theory of operators. The Fourier and Fourier Stieltjes algebras of a locally compact group G, A(G) and B(G) respectively, can be endowed with a natural operator space structure, as preduals of von Neumann algebras. She is interested in investigating the properties of these algebras in this framework.
Tianxuan Miao's research interest is in abstract harmonic analysis, an area that is the meeting ground of group theory, measure theory, Banach algebras, C*algebras, functional analysis and geometry. Their interest
centres around the study of geometric, algebraic and topological properties of certain Banach algebras associated to a locally compact group G, particularly the socalled Fourier algebra A(G) and FourierStieltjes algebras B(G), as well as the more general Banach algebras Ap(G) and Bp(G). Among some of the problems that Tianxuan works on are the Arens regularity of A(G) and Ap(G), the decomposition of Bp(G) and the characterization of Ap(G), extreme points of the unit ball of B(G), and exposed points of the set of invariant means.
Maria Grazia Viola's research lies in the area of operator algebras, with an emphasis on von Neumann algebras, C*algebras and subfactors. In some of her work she has used von Neumann algebras' techniques to solve some open problems involving C*algebras. She is also interested in free probability, combinatorics and planar algebras.
Applied Mathematics
Optimization/Operations Research
Wendy Huang's research fields are Operations Research and Statistics. In particular , her recent interest is in designing, analyzing, and implementing algorithms to solve deterministic and stochastic models in industrial engineering, management science, and computer experiments. In industrial engineering, one current work is to design heuristic ( efficient and reasonably accurate) methods for Online Scheduling Problems, which have applications in webbased technology. In management science, dynamic programming and stochastic programming models are set and solved for some supply chain and inventory problems with many uncertainties. In design and analysis of computer experiments, which is used widely in engineering design to globally optimize an expensive function, stochastic process simulation is used. Properties of the model are studied, and some computational tests are under progress.
Liping Liu's research areas are numerical analysis and operations research. In numerical analysis, she works on superconvergence analysis and a posteriori error estimates for the finite element method of solving a class of intergodifferential equations and a class of nonlinear elliptic partial differential equations, such as, nonlinear stationary heat conduction problems in anisotropic and nonhomogeneous media. She is also investigating symmetric pyramidal finite elements that do not produce an artificial anisotropy in 3D. In operations research, she is interested in optimality conditions for nonsmooth mathematical programming, and the development of, and error analysis for, numerical methods for optimal control problems governed by partial differential equations.
Probability and Statistics
Deli Li's research interest is in probability theory, particularly with stochastic
modelling, which arises from such diverse problems as in predictions of wind flow, pricing of stock options, analyzing complex computer systems, or traffic flow in communication networks. The main focus of his research is on the longterm
behaviour of stochastic models, including stochastic approximation procedures that arise in stochastic differential equations. In particular, he is focusing on the following two main objectives: (i) asymtotic behaviour for hierarchical models; (ii) almost sure and weak convergence of random processes.
Deli Li was also Lakehead's Distinguished Research of Year in 2010. In the photo below, he accepts the award from VP Rui Wang and Dr. Peter Hollings.