# Areas of Faculty Research

## Mathematics: | ## Statistics: |

## Mathematics:

### Algebra

**Topics**: associative and nonassociative ring theory, enveloping algebras, graded rings, group rings, Hopf algebra, infinite group theory, Lie algebras and representation theory, loop theory, module theory.

**Faculty**: Bahturin, Goodaire, Kotchetov, Martinez-Pedroza, Parmenter, Usefi, Zhou

**More information**: Atlantic Algebra Centre

### Analysis

**Topics**: approximation theory, fixed point theorems, geometric analysis, harmonic and complex analysis, locally convex spaces, nonlinear analysis, nuclear and barrelled spaces, operator algebras and K-theory, operator theory, summability theory.

**Faculty**: Brunner, Merkli, Niu, Ou, Watson, Xiao, Ye, Zhao

### Combinatorics

**Topics**: colourings of designs and graphs, computational combinatorics, covering and packing designs, design theory, graph factorizations and decompositions, graph labellings, graph searching, graph theory, pursuit evasion games, resolvable designs, Skolem sequences, transversal and group divisible designs.

**More information**: Combinatorics Group

### Differential Equations and Dynamical Systems

**Topics**: continuous and discrete dynamical systems and their applications; control theory; ordinary, functional and partial differential equations.

**Faculty**: Brunner, Foster, Hurford, Niu, Ou, Summers, Yuan, Zhao

**More information**: Differential Equations and Dynamical Systems Group

### Fluid Mechanics

**Topics**: boundary-layer theory, discrete vortex methods, flow induced vibrations, geophysical fluid dynamics, Navier-Stokes problems, turbulence, viscous flow.

**More information**: Fluid Mechanics Group

### Geometry and Topology

**Topics**: classifying spaces and equivariant homotopy theory, cofibrations, equivariant cohomology theories, fibrations, geometric group theory, groups of self homotopy equivalences, Lie groups, low dimensional topology, metric spaces of non-positive curvature, moduli spaces, Nielsen numbers, symplectic geometry and hamiltonian actions, topological quantum field theories.

**Faculty**: Baird, P. Booth, Heath, Martinez-Pedroza

### Mathematical Methods and Modelling / Numerical Optimization

**Topics**: asymptotics, mathematical/numerical modelling of biological systems, neural networks, numerical optimization, perturbation methods, variational methods.

**Faculty**: Alam, Foster, Haynes, Hurford, Kocabiyik, Kondratieva, Ou, Sadov, Summers, Yuan, Zhao

### Mathematical Physics

**Topics**: black hole physics, quantum mechanics, quantum dynamical systems, quantum resonance theory, general relativity, theoretical space physics.

**Faculty**: I. Booth, Kondratieva, Kunduri, Merkli, Niu, Radford, Sadov, Summers, Ye

### Numerical Analysis and Scientific Computation

**Topics**: adaptive wavelet methods, lifting scheme, finite difference methods for ordinary and partial differential equations, moving mesh methods, multigrid methods, numerical linear algebra, Volterra integral and integro-differential equations.

**Faculty**: Alam, Brunner, Foster, Haynes, Kocabiyik, Sadov

Statistics:

### Biostatistics

**Topics**: familial models, longitudinal design and analysis of clinical trials, generalized quasi-likelihood inference, longitudinal models, missing data models, multiple comparison, survival analysis.

**Faculty**: Abarin, Cigsar, Fan, Oyet, Yilmaz

### Business and Industrial Statistics

**Topics**: experimental design, process and quality control, quality management.

**Faculty**: Cigsar, Oyet, Variyath

### Econometric Models

**Topics**: binary and count panel data models, dynamic probit and logit models, generalized quasi-likelihood inferences, linear dynamic mixed models, measurement errors.

**Faculty**: Abarin, Fan, Loredo-Osti, Oyet

### Environmental and Financial Processes

**Topics**: regression models for time series data, spatial temporal models, volatility models for discrete and continuous time series.

**Faculty**: Loredo-Osti, Variyath

### General Applied Statistics

**Topics**: capture re-capture models, categorical data analysis, classification, lifetime data models, linear and non-linear regression models, stock assessment in fisheries.

**Faculty**: Abarin, Cadigan, Cigsar, Fan, Gadag, Loredo-Osti, Oyet, Variyath, Ye, Yilmaz

### Non-Parametric Statistics

**Topics**: density estimation, kernel inferences, non-parametric regression, wavelet inference, semi-parametric regression.

### Sampling

**Topics**: familial models for survey data, longitudinal models for survey data, successive substitution sampling.

**Faculty**: Abarin, Cadigan, Cigsar, Loredo-Osti, Yilmaz

### Statistical Genetics

**Topics**: analysis of complex traits, genetic architecture pedigree, genomic data, pattern recognition for high-dimensional data.

**Faculty**: Loredo-Osti, Yilmaz

### Theory of Statistics and Probability

**Topics**: branching process, brandit problems, distribution theory, inference for statistic process, order statistics, power divengence statistics, probability, robust inference in the presence of outliers.

**Faculty**: Abarin, Cigsar, Fan, Gadag, Loredo-Osti, Oyet, Wang, Ye, Yilmaz