Mathematics

Overview

It provides a broad background in mathematics and mathematical sciences. Students can choose to focus their research in one of the three areas: Pure Mathematics , Applied Mathematics, and Probability and Statistics. 

A candidate for a PhD degree is expected to demonstrate mastery of knowledge in the chosen discipline and to synthesize and create new knowledge, making an original and substantial contribution to the discipline.

Research Foci

Algebra and Number Theory

Representation theory of reductive groups, quantum groups, infinite dimensional Lie groups and Lie algebras and applications to mathematical physics and number theory.

Geometry and Topology

Algebraic geometry, differential geometry, low dimensional topology, equivariant topology, combinatorics and combinatorial topology, and geometrical structures in mathematical physics.

Analysis and Differential Equations

Complex analysis, exponential asymptotics, functional analysis, harmonic analysis, wavelets analysis, nonlinear equations and dynamical systems, integrable systems, fluid dynamics, and inverse problems.

Applied and Computational Mathematics

Modeling and simulation in fluid dynamics and materials science, computational fluid dynamics, multiscale modeling, kinetic theory, atomistic simulations, image processing, computational harmonic analysis, inverse problems and wave propagation, graph theory, optimization, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, numerical analysis, parallel algorithms, and numerical software.

Financial Mathematics

Asset allocation/management, derivative modeling, pricing and hedging and division or firm-wise risk management are traditional research areas. The recent trend of financial mathematics research is data driven, adopting methodologies of big data and machine learning.

Probability and Statistics

Time series and dependent data, resampling methodology, stochastic processes and stochastic analysis, and survival analysis, random matrix, statistical physics and high-dimensional statistics.

Data Science

Financial statistics, econometrics, statistical machine learning, statistical genetics and genomics, computational biology and bioinformatics, error in variables model, generalized linear models; biological and medical statistics, topological and geometric methods in data analysis.; mathematical data analysis, in terms of accuracy, running time, memory efficiency, scalability, or other computational measures.

Learning Outcomes

On successful completion of the PhD in Mathematics from The Hong Kong University of Science and Technology , graduates will be able to:

• Be able to conduct independent and original research in mathematics;
• Demonstrate mastery of knowledge in the chosen discipline of mathematics;
• Be able to synthesize and create new knowledge and to make original and substantial contributions to the discipline of mathematics;
• Demonstrate a broad knowledge in mathematics and mathematical sciences; and
• Demonstrate effective communication skills in presenting and publishing findings in mathematics.