Joining the Department as a postgraduate is certainly a good move. The Department maintains strong research in both pure and applied mathematics, as well as the traditional core of a mathematics department. What makes our Department different is the equally strong research in fluid mechanics, scientific computation and statistics.
The quality of research at the postgraduate level is reflected in the scholarly achievements of faculty members, many of whom are recognized as leading authorities in their fields. Research programs often involve collaboration with scholars at an international level, especially in the European, North American and Chinese universities. Renowned academics also take part in the Department's regular colloquia and seminars. The faculty comprises several groups: Pure Mathematics, Applied Mathematics, Probability and Statistics.
Mathematics permeates almost every discipline of science and technology. We believe our comprehensive approach enables inspiring interaction among different faculty members and helps generate new mathematical tools to meet the scientific and technological challenges facing our fast-changing world.
The MPhil program seeks to strengthen students' general background in mathematics and mathematical sciences, and to expose students to the environment and scope of mathematical research. Submission and successful defense of a thesis based on original research are required.
Algebra and Number Theory
The theory of Lie groups, Lie algebras and their representations play an important role in many of the recent development in mathematics and in the interaction of mathematics with physics. Our research includes representation theory of reductive groups, Kac-Moody algebras, quantum groups, and conformal field theory. Number theory has a long and distinguished history, and the concepts and problems relating to the theory have been instrumental in the foundation of a large part of mathematics. Number theory has flourished in recent years, as made evident by the proof of Fermat's Last Theorem. Our research specializes in automorphic forms.
Analysis and Differential Equations
The analysis of real and complex functions plays a fundamental role in mathematics. This is a classical yet still vibrant subject that has a wide range of applications. Differential equations are used to describe many scientific, engineering and economic problems. The theoretical and numerical study of such equations is crucial in understanding and solving problems. Our research areas include complex analysis, exponential asymptotics, functional analysis, nonlinear equations and dynamical systems, and integrable systems.
Geometry and Topology
Geometry and topology provide an essential language describing all kinds of structures in Nature. The subject has been vastly enriched by close interaction with other mathematical fields and with fields of science such as physics, astronomy and mechanics. The result has led to great advances in the subject, as highlighted by the proof of the Poincaré conjecture. Active research areas in the Department include algebraic geometry, differential geometry, low-dimensional topology, equivariant topology, combinatorial topology, and geometrical structures in mathematical physics.
The focus is on the development of advance algorithms and efficient computational schemes. Current research areas include: parallel algorithms, heterogeneous network computing, graph theory, image processing, computational fluid dynamics, singular problems, adaptive grid method, rarefied flow simulations.
The applications of mathematics to interdisciplinary science areas include: material science, multiscale modeling, mutliphase flows, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, astrophysics and space science.
Probability and Statistics
Statistics, the science of collecting, analyzing, interpreting, and presenting data, is an essential tool in a wide variety of academic disciplines as well as for business, government, medicine and industry. Our research is conducted in four categories. Time Series and Dependent Data: inference from nonstationarity, nonlinearity, long-memory behavior, and continuous time models. Resampling Methodology: block bootstrap, bootstrap for censored data, and Edgeworth and saddle point approximations. Stochastic Processes and Stochastic Analysis: filtering, diffusion and Markov processes, and stochastic approximation and control. Survival Analysis: survival function and errors in variables for general linear models. Probability current research includes limit theory.
This is one of the fastest growing research fields in applied mathematics. International banking and financial firms around the globe are hiring science PhDs who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. The trend has been accelerating in recent years on numerous fronts, driven both by substantial theoretical advances as well as by a practical need in the industry to develop effective methods to price and hedge increasingly complex financial instruments. Current research areas include pricing models for exotic options, the development of pricing algorithms for complex financial derivatives, credit derivatives, risk management, stochastic analysis of interest rates and related models.
The Department enjoys a range of up-to-date facilities and equipment for teaching and research purposes. It has two computer laboratories and a Math Support Center equipped with 100 desktop computers for undergraduate and postgraduate students. The Department also provides an electronic homework system and a storage cloud system to enhance teaching and learning.
To assist computations that require a large amount of processing power in the research area of scientific computation, a High Performance Computing (HPC) laboratory equipped with more than 200 high-speed workstations and servers has been set up. With advanced parallel computing technologies, these powerful computers are capable of delivering 17.2 TFLOPS processing power to solve computationally intensive problems in our innovative research projects. Such equipment helps our faculty and postgraduate students to stay at the forefront of their fields. Research projects in areas such as astrophysics, computational fluid dynamics, financial mathematics, mathematical modeling and simulation in materials science, molecular simulation, numerical ocean modeling, numerical weather prediction and numerical methods for micromagnetics simulations all benefit from our powerful computing facilities.