Transcript CZ2105 Lecture 2 - National University of Singapore

SPS Talk
Interests of 63
Mathematics Faculty
http://ww1.math.nus.edu.sg/staff.aspx
ASLAKSEN, Helmer Differential geometry, Lie groups, astronomy, mathematics in art
BAO Weizhu Bose-Einstein condensation, multiscale modelling and simulation, CFD,
numerical analysis/scientific computing
BERRICK, A Jon Algebraic topology, K-theory, cohomology of groups
CHAN Heng Huat Analytic number theory, basic hypergeometric series, elliptic
functions, modular forms and modular equations, applications of modular equations
CHEN Hsiao Yun, Louis Applied probability, Stein’s method, computational biology
CHEN, Oliver Financial mathematics with a concentration on credit risk and derivative
pricing
CHEW Tuan Seng Nonabsolute integrals and their applications, The Riemann approach
to integration in infinite-dimensional spaces
CHIN, CheeWhye Arithmetic algebraic geometry, automorphic representations, Lfunctions.
CHOI Kwok Pui Martingale inequalities, Poisson approximation, Prophet inequalities
CHONG Chi Tat Recursion/Computability Theory
CHU Delin Scientific and parallel computing, numerical linear algebra and numerical
analysis, systems and control
CHUA Seng Kee Sobolev spaces, Fourier analysis, classical real analysisSobolev
spaces, Fourier analysis, classical real analysis
DAI Min Financial mathematics, applied partial differential equations, numerical analysis
and scientific computation
FENG Qi Set theory
GOH Say Song Wavelet theory and applications, univalent functions
HINZ, Juri Asset pricing theory, arising from applications to energy related commodities,
services and permissions
JI Hui computer vision, visual psychophysics, robotic navigation
JIN Hanqing Mathematical finance, operation research, and stochastic analysis
KOH Khee Meng Partially ordered sets, lattice theory, graph theory
LANG Mong Lung Finite group theory
LAWTON, Wayne M Geometric and Harmonic Analysis, Mathematical Physics, Systems
Engineering
LEE Seng Luan Spline functions, wavelet theory and applications
LEE Soo Teck Representation theory
LEONG Yu Kiang Asymptotic analysis of matrix products, history of the genesis of
modern mathematical ideas
LEUNG Ho Hon, Denny Banach spaces, Banach lattices
LEUNG Ka Hin Ordered rings, ring theory, quadratic forms, combinatoric designs
LEUNG Man Chun Partial differential equations, Riemannian geometry, analysis on
manifolds
LEUNG Pui Fai, Fred Differential geometry
LIN Ping Scientific computing and numerical analysis, computational fluid mechanics,
atomistic-to-continuum modeling and analysis, ordinary and partial differential equations
with constraints, singular perturbation
LOKE Hung Yean Number theory, representations of Lie groups
LOU Jiann Hua Limit theorems and inequalities in probability, self-similar processes,
Brownian excursion
MA Siu Lun, Leo Combinatorial designs and difference sets, binary sequences and
arrays, algebraic combinatorics, Hadamard matrices
McINNES, Brett T Applications of differential geometry in cosmology, particle theory,
string theory
NATARAJAN Karthik Operations research, Optimization under uncertainty
NIEDERREITER, Harald Coding theory, cryptology, numerical analysis, simulation
methods, number theory, finite fields, discrete Mathematics, applied algebra
PANG Yu Hin, Peter Differential geometry, differential equations
POH Kheng Siong, Roger The closed-set lattice of a graph, the path-chromatic numbers
of graphs
QUEK Tong Seng Commutative harmonic analysis
SHEN Zuowei Approximation theory, wavelet theory and applications, mathematical
Imaging
STEPHAN, Frank Theoretical computer science and mathematical logic
SUN Defeng Optimization, operations research
SUN Yeneng Analysis, probability theory and their applications in economics and finance
TAN Choon Ee, Roger Extrapolation methods, finite and continuous perturbations of
matrix, eigensystems, numerical analysis
TAN Eng Chye Representation theory of Lie groups and Lie algebras, invariant theory
TAN Hwee Huat Geometric modelling, wavelet theory and applications
TAN Kai Meng Representation theory of symmetric groups and related algebras
TAN Ser Peow Geometric topology, geometric structures on manifolds
TAN, Victor Automorphic forms and representations, algebraic number theory, modular
forms and elliptic functions, combinatorial designs and difference sets
TANG Wai Shing Operator theory and operator algebras, wavelet analysis
TAY Tiong Seng Rigidity of structures, combinatorics
TAY Y.C. Performance modeling, distributed computing, database systems
TO Wing Keung Differential geometry, several complex variables
TOH Kim Chuan Scientific computing, numerical optimization
WONG Yan Loi Low-dimensional topology
WU Jie Algebraic topology-homotopy theory, combinatorial group theory, Hopf algebras,
configuration spaces, modular representation theory
XING Chaoping Number theory, algebraic curves, coding and cryptography, QuasiMonte Carlo methods
XU Xingwang Partial differential equations, geometric analysis
YANG Yue Recursion theory, Models of arithmetic
YIP, Andy M Variational PDE methods in image restoration, data mining algorithms
ZHANG De-Qi Algebraic geometry
ZHANG Louxin Applied discrete Mathematics, theoretical computer science,
computational Biology and Bioinformatics
ZHAO GongYun Game theory, operational research
ZHU Chengbo Representation theory of Lie groups
Challenges
so many colleagues
so many interests
specialized jargon
Mathematics
differs from both empirical sciences
(physics, chemistry, biology)
and observational sciences
(geology, meteorology, astronomy)
in its deductive methodology.
Mathematics
deals with two subjects :
Computation
and
Shape
Computation
numerical analysis algebra statistics
probabilities scientific computing
financial prices differential equations
functions : splines and wavelets
combinatorics
Fourier analysis
set theory
signals and image processing
functions : splines & wavelets
robotics recursion theory
logic
Shape - Geometry
Classical (Synthetic)
Algebraic (Analytic)
Differential
Lie Groups and Symmetries
Banach Spaces Complex (Analysis)
Convex Geometry (Game Theory,
Linear Programming)
Topology – General and Algebraic
Arithmetic Geometry