Our research groups in the areas of applied and computational mathematics include:

Computational Biology & Bioinformatics 

The group conducts research in modern biology problems by tapping on strengths in combinatorics, probability and statistics. Our objective is to develop mathematical understanding of biology problems to push the research frontiers in life sciences. Our research projects include bioinformatics approach to reconstructing an old ancestral genome of all placental mammals,  applying pattern and run statistics to detecting functional signals in biological sequence and identifying optimal spaced seeds for homology search,   genome rearrangement, microarray analysis of cancer transcriptomes, and modeling of biological complexity evolution of proteins and its domains.

Imaging Science & Computer Vision 

It is a multidisciplinary research group that emphasizes the synergy of mathematics, engineering and computer science in the areas of imaging science, geometric modelling, information visualization and computer vision. The objective is to develop the mathematical understanding with new ideas and methods that push the frontiers of scientific research in these areas and their applications. The main research topics include wavelets and PDE methods in imaging science, time-frequency and scale-space methods in signal and image processing, discrete geometry, computer graphics and visualization, and image understanding and computer vision.

• GOH Say Song (PhD Michigan)

• JI Hui (PhD Maryland)

• Wayne LAWTON (PhD Wesleyan)

• LEE Seng Luan (PhD Alberta)

• SHEN Zuowei (PhD Alberta)

• TAN Hwee Huat (PhD Adelaide)

• YIP Andy M (PhD UCLA)

Mathematical Finance & Mathematical Economics 

Mathematical concepts and techniques provide the language and tools for the development of modern economics and finance. On the other hand, the theoretical advancement of economics and finance also stimulates the development of new mathematics. The research group works in the interface of these areas. In particular, group members have worked on the following topics: pricing of options via PDE method, credit risk, risk identification and portfolio analysis in a large financial market, stochastic controls and portfolio selection, games with imperfect information or with many players or with location problems, general risk and uncertainty, model of complete insurance, random matching of economic agents, incentive compatibility problems in a large market with asymmetric information.

Numerical Analysis & Scientific Computing 

Computation is now becoming the third paradigm to study problems arising from science and engineering along with theory and experiment as the other two. The key issue for computation is to design and analyze efficient, accurate and robust numerical methods.  Faculty members have worked and will continue to work on: computational fluid dynamics, especially for complex fluids; computational quantum and plasma physics; control theory; computational biology and bioinformatics; numerical linear algebra; multi-scale modeling and simulation; computational methodology; analysis of finite element and spectral methods; etc.

• BAO Weizhu (PhD Tsinghua)   
• CHU Delin (PhD Tsinghua)
• LIU Jie (PhD Maryland)
• TAN Roger Choon Ee (PhD La Trobe)
• TOH Kim Chuan (PhD Cornell)
• YIP Andy M (PhD UCLA)

Optimization/ Mathematical Programming

It is a major branch of modern science focusing on modeling and finding the optimal solution, or the best course of action, for decision problems (typically from economics, management, and engineering) that are constrained by limited resources. The research group works mainly on continuous optimization, possibly with stochastic variables. The strength is on the mathematical analysis, design and implementation of algorithms, and applications of linear and nonlinear (semidefinite) conic programming. The main research topics include interior point methods, nonsmooth Newton methods, augmented Lagrangian methods, log-barrier decomposition methods, computational optimization techniques such as iterative methods for large linear systems of equations, and applications of conic programming to study stochastic problems.

• Karthik NATARAJAN (PhD Singapore-MIT Alliance)

• SUN Defeng (PhD Chinese Acad. Sci.) 

• TOH Kim Chuan (PhD Cornell)

• ZHAO Gong Yun (PhD Wuerzburg)