Research Highlights

Research Highlights

An archive of research articles contributed by our faculty members to various scientific publications and Faculty of Science annual reports/newsletters.

2024

Naked Singularity Censoring with Anisotropic Apparent Horizon

Work of Assistant Professor An Xinliang

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The Critical 2d Stochastic Heat Flow

Work of Professor Caravenna Francesco, Professor Sun Rongfeng and Professor Zygouras, Nikos

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Siamese cooperative learning for unsupervised image reconstruction from incomplete measurements

Work of Associate Professor Yuhui Quan, Xinran Qin, Assistant Professor Tongyao Pang and Professor Hui Ji

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Curvature Blow-up and Mass Inflation in Spherically Symmetric Collapse to a Schwarzschild Black Hole

Work of Assistant Professor An Xinliang and Professor Gajic Dejan

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Small Scale Formations in the Incompressible Porous Media Equation

Work of Professor Alexander Kiselev and Associate Professor Yao Yao

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Deep Learning via Dynamical Systems: An Approximation Perspective

Work of Assistant Professor Qianxiao Li, Ting Lin and Professor Zuowei Shen

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Determinantal Point Processes Based on Orthogonal Polynomials for Sampling Minibatches in SGD

Work of Assistant Professor Ghosh, Subhroshekhar

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Portfolio Diversification and Model Uncertainty: A Robust Dynamic Mean‐Variance Approach

Work of Associate Professor Zhou Chao

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Deep Learning from A Dynamical Viewpoint

Work of Assistant Professor Li Qianxiao

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2021

Flows on the PGL(V)-Hitchin component
Dr Zhang Tengren

An energy-stable finite element method for the simulation of moving contact lines in two-phase flows
Professor Ren Weiqing

Identifying the Best List of Items under the Cascading Bandits Model
Dr Zixin Zhong (Math), Dr Wang Chi Cheung (ISEM), Associate Professor Vincent Tan (Math, ECE)

Emergence of Apparent Horizon in Gravitational Collapse
Assistant Professor An Xinliang

Burnett spectral method for the Boltzmann equation
Assistant Professor Cai Zhenning

Are Complete Information Dynamic Games Solvable?
Professor Sun Yeneng

Modelling and Simulation for Solid-State Dewetting in Materials Science
Professor Bao Weizhu

Archimedean non-vanishing, cohomological test vectors, and standard L-functions of GL_2n: complex case
Dr Tian Fang Yang, Research Fellow

Statistical inference for online learning
Assistant Professor Tong Xin

An Application of the Weak Gravity Conjecture
Professor Brett Mcinnes

Characters of some unitary highest weight representations via the theta correspondence
Research Fellow, Dr Allan Merino

Portfolio Optimization with Non-linear Price Impact
Assistant Professor Marko Weber

Gaussian Determinantal Processes: A new model for directionality in data
Assistant Professor Subhro Ghosh

Two-dimensional Kardar-Parisi-Zhang (KPZ) equation in the subcritical regime
Associate Professor Sun Rongfeng

Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane
Professor Tan Ser Peow

Distinguished limits of the navier slip model for moving contact lines
Professor Ren Weiqing

A surface with discrete and non-finitely generated automorphism group
Professor Dinh Tien Cuong 

Twisting index theoretical modular invariants by projective vector bundles
Associate Professor Han Fei

Gaussian Complex Zeros, Equilibrium Measures and Forbidden Regions
Assistant Professor Subhro Ghosh

A Fast Frequent Directions Algorithm for Low Rank Approximation
Associate Professor Chu Delin

Modular Forms and K-Colored Generalized Frobenius Partitions
Professor Dai Min

Modular Forms and K-Colored Generalized Frobenius Partitions
Professor Chan Heng Huat

Tumor angiogenesis: A study using a chemotaxis-haptotaxis model
Associate Professor Peter Pang

Monte Carlo algorithm for large spatial models      
Assistant Professor Tong Xin

Modeling seasonality and serial dependence of electricity price curves with warping functional autoregressive dynamics                                                                    
Associate Professor Chen Ying

Duality for Spherical Representations in Exceptional Theta Correspondences
Professor Loke Hung Yean

Numerical Methods for the Logarithmic Schrodinger Equation
Professor Bao Weizhu

Understanding Deep Learning through Dynamics
Presidential Young Professor Li Qianxiao

Predicting Kinase Inhibitors Using Bioactivity Matrix Derived Informer Sets
Peng Tsu Ann Assistant Professor Lee Ching-pei

Equivalence of Stochastic and Deterministic Mechanisms
Goh Keng Swee Professor Sun Yeneng

Affine actions with Hitchin linear part
President’s Assistant Professor Zhang Tengren

Second-order BSDE under monotonicity condition and liquidation problem under uncertainty
Assistant Professor Zhou Chao

Low-dimensional lonely branching random walks die out
Associate Professor Sun Rongfeng

Portfolio optimization with non-linear price impact
Assistant Professor Marko Weber 

The Effect of Batch Normalization on Gradient Descent
Professor Shen Zuowei and Assistant Professor Li Qianxiao

Conditional Expectation and Conditional Distribution of Correspondences
Professor Sun Yeneng

Max-norm optimization for robust matrix recovery
Professor Toh Kim Chuan

Polarized symmetries of algebraic manifolds
Professor Zhang De-Qi

How to see clusters in an evolutionary network
Professor ZHANG Louxin

Local root numbers and spectrum of the local descents for orthogonal groups: p-adic case
Assistant Professor ZHANG Lei

Global boundedness of solutions to a chemotaxis-haptotaxis model
Associate Professor Peter PANG

Degrees containing members of thin Pi^0_1 classes are dense and co-dense
Professor Yang Yue

A long chain of P-points
Associate Professor Dilip Raghavan

Portfolio selection with capital gains tax, recursive utility, and regime switching
Professor Dai Min

The automorphic discrete spectrum of Mp(2n)
Professor Gan Wee Teck

Refined estimates for simple blow-ups of the scalar curvature equation on S^n
Associate Professor Leung Man Chun

Stealthy hyperuniform processes: maximal rigidity and the bounded holes conjecture
Assistant Professor Subhroshekhar Ghosh

Recursive diffeomorphism-based regression for shape functions
Assistant Professor Yang Haizhao

Representations of real or p-adic reductive groups
Professor Loke Hung Yean

Dynamic directed random matching
Professor Sun Yeneng

The mathematics of measuring financial risks
Associate Professor Leung Ho Hon, Denny

How does weather forecast work mathematically?
Assistant Professor Tong Xin

Unique ergodicity for foliations in P^2 with an invariant curve
Professor Dinh Tien Cuong

Stochastic Control for a Class of Nonlinear Kernels and Applications
Assistant Professor Zhou Chao

Numerical simulation of Landau damping
Assistant Professor Cai Zhenning

Hyperbolic jigsaws and families of pseudomodular groups
Professor Tan Ser Peow

Nonintersecting Brownian bridges between walls
Assistant Professor Wang Dong

q-Decomposition numbers
Associate Professor Tan Kai Meng

Eigenvalue Embedding of Undamped Vibroacoustic Systems with No-spillover
Associate Professor Chu Delin

The inductive strength of Ramsey’s theorem for pairs
Professor Chong Chi Tat and Professor Yang Yue

Rationality of homogeneous varieties
Associate Professor Chin Chee Whye and Professor Zhang De-Qi

On a class of rotationally symmetric p-harmonic maps
Associate Professor Leung Man Chun

The order structure of special ultrafilters on the natural numbers
Dr Dilip Raghavan

Economic equilibrium and conditional expectation of correspondences
Professor Sun Yeneng

Jordan property for automorphism groups of projective varieties
Professor Zhang De-Qi

Holography of the QGP Reynolds number
Professor Brett Mcinnes

Theta lifts of tempered representations
Professor Gan Wee Teck

An efficient semismooth Newton based algorithm for convex clustering
Professor Sun Defeng and Professor Toh Kim Chuan

Double Pieri algebras and iterated Pieri algebras for the classical groups
Professor Lee Soo Teck

Moderate deviation analysis for classical communication over quantum channels
Associate Professor Vincent Tan

Jumps in equity index returns before and during the recent financial crisis
Professor Steven Kou

Moment map flows and the Hecke correspondence for quivers
Assistant Professor Graeme Wilkin

Mathematical properties of a cancer invasion model
Associate Professor Peter Pang

Degenerate p-Laplacian equations
Associate Professor CHUA Seng Kee

Polynomial chaos and scaling limits of disordered systems
Associate Professor SUN Rongfeng

Deciding Parity Games in Quasipolynomial Time
Professor Frank Stephan

Reconciling the Species and Gene evolutionary trees
Professor ZHANG Louxin

Multiscale Methods and Analysis for the Dirac Equation
Professor BAO Weizhu

Unipotent Representations of Real Classical Groups
Professor Zhu Chengbo

A Wavelet Frame Method with Shape Prior for Ultrasound Video Segmentation
Professor Shen Zuowei

The Supporting Halfspace Quadratic Programming Strategy for the Dual of the Best Approximation Problem
Dr Jeffrey Pang 

The homotopy types of moment-angle complexes for flag complexes
Professor Wu Jie

Market Closure and Liquidity Premia
Professor Dai Min

Incremental regularized least squares for dimensionality reduction of large-scale data
Associate Professor Chu Delin

A Mathematical Theory of Fintech
Professor Steven Kou

Estimating Defocus Blur via Rank of Local Patches
Associate Professor Ji Hui

Twist Automorphic Descent on the Jacquet-Langlands correspondence
Dr Zhang Lei

A practical optimisation algorithm for big data applications
Dr Vincent Tan
(Source: Faculty of Science Research Highlights)

Nodal-continuous finite element methods of very weak solutions of curlcurl-graddiv eigenvalue interface problems
Associate Professor Roger Tan

Improved Bounds on Sidon Sets via Lattice Packings of Simplices
Dr Vincent TAN

Modelling rare events in complex systems
Professor Ren Weiqing
(Source: Faculty of Science Research Highlights)

The Theta Correspondence
Professor Gan Wee Teck

A highly efficient method for solving Lasso problems
Dr LI Xudong, Professor Sun Defeng and Professor Toh Kim Chuan

What is the weather tomorrow?
Dr Tong Xin
(Source: Faculty of Science Research Highlights)

A Fast Program for Verification of Phylogenetic Network Models
Professor Zhang Louxin

The Anti-Field-Descent Method
Professor Leung Ka Hin

Complex Hénon maps in higher dimension
Professor Dinh Tien Cuong

Data assimilation in high dimensions
Dr Tong Xin

Universality of nonintersecting Brownian motions with a wall
Dr Wang Dong

Decomposition numbers for symmetric groups
Associate Professor Tan Kai Meng

Mathematics of Black Holes and Heavy Ion Collisions
Professor Brett Mcinnes

The Continuum Disordered Pinning Model
Associate Professor Sun Rongfeng

A longstanding problem in algebraic geometry
Professor Zhang De-Qi

Hubbard model and Bose-Einstein condensate
Professor Bao Weizhu

Counting motifs in the human interactome
Associate Professor Zhang Louxin
(Source: Faculty of Science Research Highlights)

Fluid structure interaction
Dr Liu Jie
(Source: Faculty of Science Research Highlights)

Optimal trend-following trading rules
Professor Dai Min
(Source: Faculty of Science Research Highlights)

Memory allocation for computer systems
Professor Tay Yong Chiang
(Source: Asia Pacific Mathematics Newsletter)

Ramsey’s Theorem, Reverse Mathematics and Nonstandard Models
Professor Chong Chi Tat and Professor Yang Yue
(Source: Asia Pacific Mathematics Newsletter)

Wetting transition on patterned surfaces
Associate Professor Ren Weiqing
(Source: Faculty of Science Research Highlights)

The Science behind our Scientists
Professor Chong Chi Tat and Professor Yang Yue
(Source: Faculty of Science, Omniscience)

Invariants of theta correspondences
Associate Professor Loke Hung Yean
(Source: Faculty of Science Research Highlights)

Howe Duality Conjecture
Professor Gan Wee Teck
(Source: Innovation Magazine, Volume 13 No. 2, 2014)

The Howe Duality Conjecture
Professor Gan Wee Teck
(Source: Asia Pacific Mathematics Newsletter, Oct 2014)

Deblurring the unknown
Associate Professor Ji Hui
(Source: Faculty of Science Research Newsletter, Dec 2014)

Numerical Methods for Blind Image De-convolution
Associate Professor Ji Hui
(Source: Innovation Magazine, Volume 13 No. 2, 2014)

Quantitative Finance and Risk Management
Professor Steven Kou
(Source: Innovation Magazine, Volume 13 No. 2, 2014)

Large-Scale Matrix Optimization Problems
Professor Sun Defeng and Professor Toh Kim Chuan
(Source: Innovation Magazine, Volume 13 No. 2, 2014)

Identities on Hyperbolic Surfaces
Professor Tan Ser Peow
(Source: Innovation Magazine, Volume 13 No. 2, 2014)

Curvature and Hyperbolicity Properties of Certain Moduli Spaces
Professor To Wing Keung
(Source: Innovation Magazine, Volume 13 No. 2, 2014)

Separating Combinatorial Principles Using Nonstandard Models
Professor Yang Yue
(Source: Innovation Magazine, Volume 13 No. 2, 2014)

Mathematics in the deluge of DNA data
Associate Professor Zhang Louxin
(Source: Faculty of Science Research Newsletter, Dec 2014)

Modelling uncertainty in financial markets
Dr Zhou Chao
(Source: Faculty of Science Research Newsletter, June 2014)

2013

Mathematical Models and Numerical Methods for Dipolar Bose-Einstein Condensates
Professor Bao Weizhu
(Source: Faculty of Science Annual Report, Academic Year 2012/13)

Blind Image De-convolution by Sparse Approximation
Associate Professor Ji Hui
(Source: Faculty of Science Annual Report, Academic Year 2012/13)

Elliptic curves, modular forms and the Langlands Programme
Professor Gan Wee Teck
(Source: Faculty of Science Research Newsletter, June 2013)

Quantitative finance after the recent financial crisis
Professor Steven Kou
(Source: Faculty of Science Research Newsletter, Dec 2013)

2012

Blind image deconvolution for a shaken photograph
Associate Professor Ji Hui
(Source: Faculty of Science Research Highlights)

The search for new Mathematical axioms
Dr Dilip Raghavan
(Source: Faculty of Science Research Newsletter, Dec 2012)

Understanding Complex Energy Landscapes and Rare Events
Associate Professor Ren Weiqing
(Source: Faculty of Science Research Newsletter, June 2012)

Scalar Curvature Flow Method Resolves Prescribed Scalar Curvature Problem
Professor Xu Xingwang
(Source: Faculty of Science Annual Report, Academic Year 2011/12)

2011

Quantitative modeling of emission markets
Associate Professor Juri Hinz 
(Source: Faculty of Science Research Highlights)

Typical Dynamics of Uni-Critical Polynomials
Professor Shen Weixiao
(Source: Faculty of Science Annual Report, Academic Year 2010/11)

Large-Scale Matrix Cone Programming
Professor Sun Defeng and Professor Toh Kim Chuan
(Source: Faculty of Science Annual Report, Academic Year 2010/11)

From Coin Tosses to the Brownian Web and Net
Dr Sun Rongfeng
(Source: Faculty of Science Research Newsletter, June 2011)

Towards Morse-Kirwan theory on singular spaces
Dr Graeme Wilkin
(Source: Faculty of Science Research Newsletter, Dec 2011)

2010

Modular Forms and Gravitational Anomaly Cancellation in String Theory
Dr Han Fei
(Source: Faculty of Science Research Newsletter, Dec 2010)

Numerical Methods for Incompressible Viscous Fluid and Fluid Structure Interaction
Dr Liu Jie
(Source: Faculty of Science Research Newsletter, June 2010)

A Socialistic Approach to Construct Solution Operator for the Boltzmann Equation in a Small Bounded Domain
Professor Yu Shih-Hsien
(Source: Faculty of Science Research Highlights)

Nonlinear Wave Propagations Over a Boltzmann Shock Profile
Professor Yu Shih-Hsien
(Source: Faculty of Science Annual Report, Academic Year 2009/10)

Multiplicity One in Symmetry Breaking
Professor Zhu Chengbo
(Source: Faculty of Science Annual Report, Academic Year 2009/10)

2009

Rigidity behind the Chaos
Professor Zhang De-Qi
(Source: Faculty of Science Annual Report, Academic Year 2008/09)

2008

Boltzmann Equation, Industry Technology Advancement, and Mathematical Analysis
Professor Yu Shih-Hsien
(Source: Faculty of Science Research Newsletter, 2008)

2007

Braids: New mathematical insights on an old topic
Professor Jon Berrick
(Source: Faculty of Science Research Newsletter, 2007)

2006

Robotic navigation through visual sensors
Associate Professor Ji Hui
(Source: Faculty of Science Research Newsletter, 2006)

2005

Total Variation Based Methods for Image Restoration
Dr Andy M. Yip
(Source: Faculty of Science Research Newsletter, 2005)