The Mathematics Department is affiliated with Trent's graduate program in Applications of Modelling in the Natural and Social Sciences (AMINSS). Prospective graduate students are encouraged to contact department members with similar research interests.
- Kenzu Abdella
Research interests: Applied Mathematics with a particular emphasis on atmospheric physics and computational fluid dynamics. In atmospheric physics the main research focus is on the parameterization of various physical processes. Recent work mainly deals with boundary and surface layer processes including turbulence and cloud physics. While most of the modelling development is carried out on a one- dimensional column model version, the final goal of the research is to develop parameterizations for use in the full three dimensional global circulation models (GCMs). My work also includes, general computational and theoretical fluid dynamics problems, numerical simulation of free surface problems and hydrodynamic stability.
- Nikolai Dokuchaev
Research interests: Mathematical finance, stochastic differential equations, partial differential equations, stochastic control. Currently I am interested in mathematical finance, including optimal portfolio selection and pricing for discrete time and continuous time market models. I am also interested in boundary value problems for parabolic equations and parabolic Ito equations, especially in existence, prior estimates, and regularity of solutions.
- Wenying Feng
Research interests: In Computer Science, I am working on the applications of mathematical and simulation modeling in the study of computer systems. Currently, I am involved in several research projects including Web caching, queuing models for network systems, functional models for software design and testing. Most of these projects are joint work with my graduate students.
In Mathematics, I am interested in the study of existence, uniqueness, multiplicity and non-existence of solutions and positive solutions for nonlinear boundary value problems by applying topological methods such as spectral, degree, coincidence degree, eigenvalue and fixed point theories. I am also working on nonlinear and semilinear spectral theories and their applications.
- Marcus Pivato
Research interests: (1) Symbolic dynamical systems, particularly cellular automata (CA), tilings, and multidimensional subshifts of finite type. Specifically: (a) Asymptotic randomization of probability measures; (b) emergence and interaction of propagating `defects' in tilings. (c) (co)homological and spectral invariants of these defect structures. (d) The hydrodynamics of particle-preserving CA.
(2) Mathematical economics, particularly game theory and social choice theory. Specifically: (a) Pyramidal democracy; (b) Relative utilitarianism (a.k.a. `range voting'); (c) Groves-Clarke `pivotal' voting mechanisms; (d) Microeconomic disequilibrium dynamics.
- Marco Pollanen
Mathematical and Computational Finance; Monte Carlo and Quasi-Monte Carlo Methods; Applied Probability; Mathematical Knowledge Management
- Reem Yassawi
Research interests: Cellular automata and symbolic dynamics.
- Bing Zhou
Research interests: Combinatorics and graph theory, particularly the colouring problems and extremal problems of graphs. Many practical problems in computer science, operation research and social science can be modelled by graph theory. The solutions of the colouring problems of graphs can be applied to scheduling problems; the solutions of the problems involving planar graphs can be applied to circuit design and network design. The methods used are mathematical deduction and computer experiment.