School of SCIENCE 8 Research Foci math.hkust.edu.hk 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. Department of Mathematics Facilities The Department enjoys a range of up-to-date computing facilities. Besides a laboratory with 40 high-end desktop PCs, there is also a High Performance Computing laboratory equipped with 200 powerful CPU- & GPUbased computer servers having 250 TFLOPS processing power and 1.5PB storage capacity. Moreover, the NVIDIA DGX SuperPOD Supercomputer in the Hong Kong campus and the Tianhe2 Supercomputer in the Guangzhou Fok Ying Tung Research Institute are also available.
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