Our research in pure mathematics can be broadly categorized under several areas.

Algebra & Number Theory 

This research group has diverse interests in algebra and number theory.  Research topics of the group members include additive and analytic number theory, algebraic K-theory, automorphic forms, L-functions, cohomology of groups, finite fields, curves over finite fields, finite group theory, representation theory of symmetric groups and related algebras. 

• CHAN Heng Huat (PhD Illinois)

• CHIN Chee Whye (PhD Princeton)

• TAN Kai Meng (PhD Cambridge)

Combinatorics & Graph Theory 

Research topics of the group members include algebraic combinatorics, graph theory, finite geometry, difference sets, rigidity of frameworks, lattice theory, as well as their applications to combinatorial designs and problems in biology such as homology detection and gene duplication in comparative genomics. 

• KOH Khee Meng (PhD Manitoba)

• LEUNG Ka Hin (PhD Berkeley)

• MA Siu Lun (PhD Hong Kong)

• TAY Tiong Seng (PhD Waterloo)

Geometry & Mathematical Physics 

The study of geometry is intertwined with that of many other mathematical areas as well as other scientific disciplines such as physics.  This group has diverse research interests in algebraic geometry, complex geometry, geometric analysis, global differential geometry and certain areas of mathematical physics, which include string theory and cosmology.

• Han Fei (PhD Berkeley)

• Brett McINNES (PhD Sydney)

• TO Wing Keung (PhD Columbia)

• ZHANG De-Qi (PhD Osaka)

Lie Groups, Lie Algebras & Representation Theory 

Symmetry plays an important role in all of mathematics and physics. The most successful applications of symmetry have employed Lie Groups, Lie Algebras and their representations.  Research topics conducted by members of this research group include classical groups, branching laws, theta correspondence and unitary representations.

• Helmer ASLAKSEN (PhD Berkeley)

• LEE Soo Teck (PhD Yale)

• LOKE Hung Yean (PhD Harvard)

• TAN Eng Chye (PhD Yale)

• ZHU Chen-Bo (PhD Yale)

Mathematical Logic & Theoretical Computer Science 

The study of mathematical logic has strong connections with foundations of mathematics and theoretical computer science.  The research areas of the logic group include set theory, computability theory, information theory and performance modeling.

• CHONG Chi Tat (PhD Yale)

• FENG Qi (PhD Penn. State)

• Frank STEPHAN (PhD Karlsruhe)

• TAY Yong Chiang (PhD Harvard)

• YANG Yue (PhD Cornell)

Partial Differential Equations & Geometric Analysis 

The interests of this research group are mainly in nonlinear partial differential equations of parabolic, elliptic and hyperbolic types. These include problems on conformal geometry and their applications to Riemannian geometry and mathematical physics; Boltzmann equation, conservation laws and nonlinear reaction-diffusion equations.

• LEUNG Man Chun (PhD Michigan)

• PANG Peter Yu Hin (PhD Illinois)

• XU Xingwang (PhD Connecticut)  

• Yu Shih-Hsien (PhD Stanford)   

Probability 

The probability group is interested in both basic and applied research in the field and has done work in Stein's method, self-similar processes, martingales, Brownian motion, Poincaré-type inequalities, limit theorems and applications to computation biology.  Current work includes normal approximation, compound Poisson approximation, Poisson process approximation, translated Poisson approximation as well as applications in probability modeling and analysis of distributions of motifs in genomes and analysis of spaced seed for biological sequence alignment.

• CHEN Louis Hsiao Yun (PhD Stanford)             

• CHOI Kwok Pui (PhD Illinois)

• SUN Rongfeng (PhD Courant, New York)

• ZHOU Wang (PhD CUHK)

Real, Functional & Harmonic Analysis 

Mathematical analysis is one of the pillars on which modern mathematics is built.  Research undertaken by members of the group includes classical analysis, Sobolev spaces, Banach space theory, operator algebras, dynamical systems, nonstandard analysis and their applications to economics.

Topology 

The research group conducts research in algebraic topology, K-theory, low-dimensional and geometric topology.  Research topics of the group members include homotopy theory, configuration spaces, braid groups and their representations, combinatorial knot theory, wild arcs, flat conformal and projective structures on surfaces and three manifolds, representation spaces of surface groups, Teichmüller theory, and dynamical systems.