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Sharjah

Faculty members at the Department of Mathematics and Statistics are involved in cutting-edge research activities in varies disciplines of applied and pure mathematics. The broadly defined areas are listed below. Further specific details can be found in the profiles of faculty members:

**Abstract Algebra:** Commutative rings, Chained rings, Prufer rings, Dedekind rings, Pseudo-valuation rings, Nonnil-Noetherian rings, Phi-commutative rings, Pi-regular rings, Zero-divisor graphs, Error correcting coding, Turbo codes and Convolution codes.

**Applied Mathematics:** Mathematical modeling, Biomathematics, Discrete dynamical systems, Modeling and simulation of biological systems, Population dynamics, Mathematical problems of imaging, Image processing with applications to noise removal, Fluid dynamics.

**Financial Mathematics:** Option pricing models, empirical performance of option pricing models, spline-based modeling, Measure-valued processes, Stochastic processes and their Applications.

**Mathematical Analysis and Topology: **Geometric theory of functions of one complex variable, Theory of minimal surfaces and its relation with univalent harmonic mappings, Banach spaces of analytic function, Weighted composition operators on weighted Hardy spaces, Special functions, Homotopy theory, loop spaces, manifold theory. Algebraic geometry, Toeplitz operators on Bergman and Hardy spaces, Products and commutativity of Toeplitz operators, fixed point theory, Functional analysis and Banach algebras.

**Numerical Analysis:** Optimal control theory, Numerical simulation, Finite element method, Computational fluid dynamic, Stability of numerical methods, Numerical modeling of phase change problems and cardiac electrophysiology.

**Ordinary & Partial Differential Equations:** Fluid dynamics, Mathematical physics, Navier-Stokes equations, Fluid flows and fluid-structure interactions, Free boundary problems, Control theory of PDEs, Mathematical aeroelasticity, Boundary/point control of coupled systems of parabolic and hyperbolic PDEs, PDE-based image processing.

**Statistics: **Time series analysis, Regression analysis, Probability distributions, Extreme value theory, Sensitivity analysis in nonlinear parameter estimation, Design of experiments, Statistical applications in health sciences, data mining.

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